From Stephanie Thompson comes a question of ballot optimization:

Derek Jeter and Larry Walker were just elected to the Baseball Hall of Fame! That got Stephanie thinking. Suppose there are 20 players on the ballot and 400 voters in a given year. Each voter can select up to 10 players for induction without voting for any given player more than once. To gain entry, a player must have been selected on at least 75 percent of the ballots.

Under these circumstances, what is the *maximum* number of players that can be inducted into the Hall of Fame?

From Dean Ballard comes another coin-related challenge — a game of “Pinching Pennies”:

The game starts with somewhere between 20 and 30 pennies, which I then divide into two piles any way I like. Then we alternate taking turns, with you first, until someone wins the game. For each turn, a player may take any number of pennies he or she likes from either pile, or instead take the same number of pennies from both piles. Each player must also take at least one penny every turn. The winner of the game is the one who takes the last penny.

If we both play optimally, what starting numbers of pennies (again, between 20 and 30) guarantee that you can win the game?

Congratulations to Kealan Vasquez of Ave Maria, Florida, winner of last week’s recent Riddler Express.

Last week, you were a coach in the Riddler Football League, and you had devised a new strategy for scoring after a touchdown. Your team would line up 2 yards away from the goal line in such a way that it could attempt either a 1-point conversion or a 2-point conversion. Your opponent could only properly defend against one of those two possibilities, so they’d have to guess.

If you attempted a 1-point conversion that was properly defended, you’d score 90 percent of the time; otherwise, you’d score 100 percent of the time. If you instead attempted a 2-point conversion that was properly defended, you’d score 40 percent of the time; otherwise, you’d score 60 percent of the time.

It was up to you to communicate to your team’s captain the probability with which they should attempt each. However, given all the spying that occurs in the League these days, you could assume that your message was overheard by your opponent, who also knew the probability of you scoring in each of the four scenarios listed above.

With all that said, what were the best offensive and defensive strategies here, and how many points would you score, on average, after each touchdown?

This was an example of a zero-sum game, meaning points were just as good for you as they were bad for your opponent. Since you and your opponent both had complete information about the probabilities, you’d pursue strategies that would result in a Nash equilibrium — that is, an effective stalemate where neither you nor your opponent would benefit from switching strategies.

Solver Ravi Chandrasekaran explored what would happen if you and your opponent tried different probabilities between always going for (or defending) 1 point vs. 2 points. Both Ravi and Kealan found that your best strategy was to go for 1 point 80 percent of the time and go for 2 points 20 percent of the time. To see why that is, suppose your opponent defends against 1 point with probability *p* and against 2 points with probability 1−*p*. How many points would you score on average? Let’s look at the four possible cases:

- You’d go for 1, and they’d defend it with probability 0.8
*p*, earning 0.9 points on average (90 percent of 1 point). - You’d go for 1, and they wouldn’t defend it with probability 0.8(1−
*p*), earning 1 point on average (100 percent of 1 point). - You’d go for 2, and they’d defend it with probability 0.2(1−
*p*), earning 0.8 points on average (40 percent of 2 points). - You’d go for 2, and they wouldn’t defend it with probability 0.2
*p*, earning 1.2 points on average (60 percent of 2 points).

Combining all these cases, the average number of points you’d get will be 0.8*p *· 0.9 + 0.8(1−*p*) · 1 + 0.2(1−*p*) · 0.8 + 0.2*p* · 1.2 = 0.96 points. Notice how all the *p*’s cancel out? That means when you go for 1 point 80 percent of the time, it doesn’t matter *what* your opponent does — you’ll score an average of 0.96 points after each touchdown. If you were to veer away from these probabilities (say, by going for 2 more often), your opponent could take advantage (by defending against the 2 more often) and lower your average number of points.

Similarly, on the defensive end, when your opponent defends against 1 point 40 percent of the time and against 2 points 60 percent of the time, you’ll again score an average of 0.96 points, no matter what your offensive strategy is. At the end of the day, you could expect to score **0.96 points** after each touchdown.

I am pleased to note that the many game theorists of Riddler Nation pointed out that, due to the defense overhearing what the offensive strategy was going to be (which was to go for 1 point 80 percent of the time), it technically didn’t matter *what* the defensive strategy was. It’s a great point! (Or was it a great 2 points?)

Congratulations to Adam Richardson of Old Hickory, Tennessee, winner of the last week’s Riddler Classic.

Last week, two delirious ducks were having a difficult time finding each other in their pond, which contained a 3×3 grid of rocks.

Every minute, each duck randomly swam from one rock to a neighboring rock in the grid — up, down, left or right but *not* diagonally. So if a duck was at the middle rock, it would next swim to one of the four side rocks with probability 1/4. From a side rock, it would swim to one of the two adjacent corner rocks or back to the middle rock, each with probability 1/3. And from a corner rock, it would swim to one of the two adjacent side rocks with probability 1/2.

If the ducks both started at the middle rock, then on average, how long would it take until they’re at the same rock again?

If the ducks were to make the same first move, they would have found each other after one minute. On the other hand, they could have gone around the rocks countless times without ever finding each other. A key insight was to realize that if you knew where the ducks were at some time, you could find a precise probability distribution for where they’d be one minute later. And because of the symmetry of the rocks, solver Jason Ash noted there were only five possible arrangements you had to keep track of:

For example, suppose after some time the ducks happen to be in the “outer across” arrangement in the above diagram. One minute later, there’s a 1/4 chance they’ll meet (if the left duck moves right and the right duck moves left), there’s a 1/4 chance they’ll switch to the “middle across” arrangement (if both ducks move down) and a 1/2 chance they’ll switch to the “diagonal outer” arrangement (if one duck moves down and the other moves horizontally).

By determining how likely the ducks transitioned between each of these different arrangements, solver Vikrant Kulkarni set up a system of equations relating the average times it took the ducks to meet from each arrangement, including the initial arrangement where both ducks were at the middle rock.

For problems like this, with random transitions between a fixed number of arrangements, many solvers, including Adam and Jason, used a technique knowns as Markov chains, which solve the very same equations Vikrant came up with. On average, the ducks will meet after **363/74**, or about 4.905, minutes.

Solver Angelos Tzelepis went one step further, finding (after 3 million simulations) the probabilities of *where* the ducks would ultimately find each other. The most likely meeting point was where they started — the rock in the middle:

Despite his mathematical prowess, Angelos did make one critical error: He incorrectly referred to the ducks as “drunk.” They were merely *delirious*.

For extra credit, you were asked to consider the case of three or more ducks: If they all started in the middle rock, on average, how long would it take until they were all at the same rock again?

Again using Markov chains, solver Laurent Lessard was able to find exact values for the cases of three, four, five and six ducks, which would respectively take on average 18.4, 66.7, 237.4 and 825.3 minutes to all meet up. As the number of ducks increased, the time it took for them to meet appeared to grow exponentially, and the computation required to find the exact result became increasingly difficult.

To find approximate solutions for the general case where there were *N* ducks, solvers Guy D. Moore and Hector Pefo used the fact that after an *odd* number of minutes the ducks would all be on one of the four sides, and after an *even* number of minutes the ducks would all be in the middle or one of the four corners.

After an odd number of minutes — when the ducks were on the sides — no side was more likely to be where they met than any of the others. That meant the probability the ducks were all together at any given minute was 1/4^{N−1}, where the minus one in the exponent came from the fact that the first duck could have been on any of the four sides, while the other *N*−1 ducks had to be on that same side. By performing a similar analysis after an even number of minutes, Guy and Hector found that *N* ducks would all meet up after approximately 2·3^{N} minutes.

That meant it would take a dozen delirious ducks approximately two years to find each other. Meanwhile, it would take a *dozen* dozen delirious ducks far longer than the age of the universe to find each other.

Those poor dozen dozen ducks.

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!

Email Zach Wissner-Gross at riddlercolumn@gmail.com.

]]>The Riddler Football League (RFL) playoffs are upon us! As the coach, you’ve devised a new strategy for scoring after a touchdown. Your team will line up 2 yards away from the goal line in such a way that it could attempt either a 1-point conversion or a 2-point conversion. (Unlike other football leagues, the distance is the same for both types of conversion, and you need not announce which you’ll be attempting.) Your opponent can only properly defend against one of those two possibilities, so they’ll have to guess.

If you attempt a 1-point conversion and the other team defends against it properly, you’ll score 90 percent of the time. If they don’t defend it properly, you’ll score 100 percent of the time.

If you instead attempt a 2-point conversion and the other team defends against it properly, you’ll score 40 percent of the time. If they don’t defend it properly, you’ll score 60 percent of the time.

To tell your team which they should attempt, your team’s offensive coordinator will communicate to your team’s captain the probability with which they should attempt each. For example, the coordinator might say: “Go for 1 with a 51 percent chance, and go for 2 with a 49 percent chance.” Using a random number generator, the captain will then ultimately decide to go for 1 point or 2 points. (Naturally, every athlete in the RFL has a random number generator handy.)

However, given all the spying that occurs in the RFL these days, you can assume that the offensive coordinator’s message will also be heard by your opponent — that means the defense knows the exact probability with which you’ll attempt either conversion. Your opponent also knows the probability of you scoring in each of the four scenarios listed above.

With all that said, what strategy will maximize the average number of points you’ll score (i.e., how often should your team go for 1 or 2)? What should your opponent’s defensive strategy be? How many points will you score, on average, after each touchdown?

After a long night of frivolous quackery, two delirious ducks are having a difficult time finding each other in their pond. The pond happens to contain a 3×3 grid of rocks.

Every minute, each duck randomly swims, independently of the other duck, from one rock to a neighboring rock in the 3×3 grid — up, down, left or right, but *not* diagonally. So if a duck is at the middle rock, it will next swim to one of the four side rocks with probability 1/4. From a side rock, it will swim to one of the two adjacent corner rocks or back to the middle rock, each with probability 1/3. And from a corner rock, it will swim to one of the two adjacent side rocks with probability 1/2.

If the ducks both start at the middle rock, then on average, how long will it take until they’re at the same rock again? (Of course, there’s a 1/4 chance that they’ll swim in the same direction after the first minute, in which case it would only take one minute for them to be at the same rock again. But it could take much longer, if they happen to keep missing each other.)

*Extra credit:* What if there are three or more ducks? If they all start in the middle rock, on average, how long will it take until they are all at the same rock again?

Congratulations to Nathan Holmes-King of Fremont, California, winner of last week’s recent Riddler Express.

Last week, you were asked to find a fraction (with a whole number numerator and denominator) that was greater than 1/2020, less than 1/2019 and with the smallest possible denominator.

Solver Amy Leblang used an algebraic approach, looking for a fraction *a*/*b* (where *a* and *b* are whole numbers) such that 1/2020 < *a*/*b* < 1/2019. Flipping all the fractions, you can rewrite this inequality as 2019 < *b*/*a* < 2020. Finally, multiplying through by *a* gives us 2019*a* < *b* < 2020*a*.

Again, our goal is to find the denominator *b* that’s as small as possible, and that will happen when *a* is also small. If we let *a* = 1, then there’s no whole number *b* that sits between 2019 and 2020, so that won’t work. But if *a* = 2, then we’re looking for a value of *b* between 4038 and 4040, which means *b* = 4039. Larger values of *a* will produce larger values of *b*, which this riddle wasn’t asking about. In other words, **2/4039** is the correct answer.

Many solvers, like Angela Zhou, observed that this question was straightforward if you knew a thing or two about Farey sequences, which are ordered sets of fractions between 0 and 1. For the Farey sequence in which all the denominators are at most 2020, the fractions 1/2020 and 1/2019 are “Farey neighbors,” meaning they’re next to right next to each other in the sequence. This riddle is effectively asking you to identify the first Farey sequence where 1/2020 and 1/2019 are *no longer* neighbors — that is, one where there’s another fraction between them. That fraction will be what’s called the mediant of the fractions on either side, generated by adding the numerators and the denominators: (1+1)/(2020+2019) = 2/4039.

Just to be extra sure that’s the right answer, solver Nolan Gannage wrote code to search all the fractions between 1/2020 and 1/2019 whose denominators were also 50,000 or less. Sure enough, the one with the smallest denominator was 2/4039.

That’s one of the Riddler maxims: “When in doubt, code it out.”

Congratulations to Austin Calico of Ashland, Kentucky, winner of the last week’s Riddler Classic.

Last week, you looked at an alphanumeric code inspired by “Gematria,” where words were assigned numerical values based on their letters. Each A was worth 1 point, each B was worth 2 points, and so on. The value of a word was then the sum of the values of its letters. For example, RIDDLER had an alphanumeric value of 70, since R + I + D + D + L + E + R became 18 + 9 + 4 + 4 + 12 + 5 + 18 = 70.

But what about the values of different numbers themselves, spelled out as words? The number 1 (ONE) had an alphanumeric value of 15 + 14 + 5 = 34, and 2 (TWO) had an alphanumeric value of 20 + 23 + 15 = 58. Both of these values were *bigger* than the original numbers.

Meanwhile, if we looked at larger numbers, 1,417 (ONE THOUSAND FOUR HUNDRED SEVENTEEN) had an alphanumeric value of 379, while 3,140,275 (THREE MILLION ONE HUNDRED FORTY THOUSAND TWO HUNDRED SEVENTY FIVE) had an alphanumeric value of 718. These values were much *smaller* than the original numbers.

If we considered all the whole numbers that were *less than* their alphanumeric value, what was the largest of these numbers?

First off, this question was a little ambiguous. The intent was to find the largest number *N* that was less than its “Gematria score” of *N*, which we’ll call *G*(*N*) — that is, *N* < *G*(*N*). However, you could also have read the question as asking for the largest value of *G*(*N*) among numbers *N* where *N* < *G*(*N*). The majority of readers answered the first question, but we’ll address both here.

Almost all solvers wrote code for this one, with the general strategy of (1) systematically describing how numbers are codified as words in English, and (2) scoring those words. A few solvers, like Cameron Shelton, took the time to work it all out by hand. In the words of Cameron, this “gives me a better feel for the problem and because I enjoy it more.” Bravo, Cameron!

Either way, the answer turned out to be **279**, or TWO HUNDRED SEVENTY NINE, which had a Gematria score of 284. To confirm this result, here’s a graph from solver Jason Ash showing the scores for the numbers from 1 to 500.

Sure enough, 279 is the last number above the dotted line, meaning it’s the greatest number to exceed its Gematria score. Interestingly, 80 is the smallest number that’s *less than* its Gematria score: EIGHTY is only worth 74 points. And for those of you who had the alternate interpretation of the original question, the number above the dotted line that’s worth the most points is 277, or TWO HUNDRED SEVENTY SEVEN, which is worth a whopping 307 points.

If you’re curious to see the scores of Gematria scores beyond those of the first 500 numbers, then solver Quoc Tran has an animation for you, showing the scores from ONE to ONE HUNDRED THOUSAND:

Finally, James Chapman took this riddle even further, solving it for multiple languages (not just English). James found that Finnish, French, and Polish each had answers just shy of 400. Dan Miller even went on to suggest using Roman numerals — maybe next time!

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!

Email Zach Wissner-Gross at riddlercolumn@gmail.com.

]]>To celebrate the new year, here’s a quick puzzle about the number 2020. Of all the fractions out there that are greater than 1/2020 but less than 1/2019, one has the smallest denominator. Which fraction is it?

(Before you ask, by “fraction” I mean that both the numerator and denominator should be whole numbers.)

From Leonard Cohen comes a puzzle at the intersection of language and mathematics:

In Jewish study, “Gematria” is an alphanumeric code where words are assigned numerical values based on their letters. We can do the same in English, assigning 1 to the letter A, 2 to the letter B, and so on, up to 26 for the letter Z. The value of a word is then the sum of the values of its letters. For example, RIDDLER has an alphanumeric value of 70, since R + I + D + D + L + E + R becomes 18 + 9 + 4 + 4 + 12 + 5 + 18 = 70.

But what about the values of different numbers themselves, spelled out as words? The number 1 (ONE) has an alphanumeric value of 15 + 14 + 5 = 34, and 2 (TWO) has an alphanumeric value of 20 + 23 + 15 = 58. Both of these values are *bigger* than the numbers themselves.

Meanwhile, if we look at larger numbers, 1,417 (ONE THOUSAND FOUR HUNDRED SEVENTEEN) has an alphanumeric value of 379, while 3,140,275 (THREE MILLION ONE HUNDRED FORTY THOUSAND TWO HUNDRED SEVENTY FIVE) has an alphanumeric value of 718. These values are much *smaller* than the numbers themselves.

If we consider all the whole numbers that are *less than* their alphanumeric value, what is the largest of these numbers?

Congratulations to Quinn Rose of Des Moines, Iowa, Mike Cromwell of Novi, Michigan, and Mark Ritchie of Cleveland, Ohio, winners of last week’s recent Riddler Express.

Last week, you were presented with three images, in which different nations’ flags had their pixels randomly rearranged. You were tasked with figuring out which flag was which.

The first flag was an even mix of red, white and blue…

…or was it blue, white and red? Quinn correctly identified it as the flag of **France**:

While there are many national flags that make use of this color palette, about 40 percent of solvers correctly identified this as France’s flag. Solver Stew Schrieffer checked this by comparing the number of pixels of each color. There were approximately an equal number of blue, white and red pixels, and the precise colors perfectly matched France’s flag. The most popular (wrong) submissions were the United Kingdom, the United States of America and Russia, each at about 15 percent.

The second flag was mostly green, followed by a mix of yellow and blue, with a pinch of white.

Mike correctly identified this as the flag of **Brazil**:

I’m happy to report that most solvers got this right. It turns out that Brazil has a very identifiable color scheme. Who knew?

The third and final flag had the greatest variety of colors and had a relatively even mix of those colors. This made it more difficult to identify.

After studying the color profile of the pixels, Mark found that there were five colors: blue and green in “equal(ish)” amounts, as well as red, white and yellow in lesser amounts. The flag that best fit this bill was **Namibia**:

About a third of respondents correctly identified Namibia, with about 20 percent guessing South Africa, 15 percent guessing the Seychelles and 10 percent guessing Turkmenistan.

Overall, this was some excellent vexillological sleuthing by Riddler Nation. Sheldon Cooper would be proud!

Congratulations to Peter Ji of Madison, Wisconsin, winner of the last week’s Riddler Classic.

Last week, you analyzed the Spelling Bee word game from The New York Times. In Spelling Bee, seven letters are arranged in a honeycomb lattice, with one letter in the center. The goal is to identify as many words that meet the following criteria:

- The word must be at least four letters long.
- The word must include the central letter.
- The word cannot include any letter beyond the seven given letters.

Note that letters can be repeated. Four-letter words are worth 1 point each, while five-letter words are worth 5 points, six-letter words are worth 6 points, seven-letter words are worth 7 points, etc. Words that use all of the seven letters in the honeycomb are known as “pangrams” and earn 7 bonus points (in addition to the points for the length of the word).

Your task was to find the seven-letter honeycomb that resulted in the highest possible game score. To be a valid choice of seven letters, no letter could be repeated, it couldn’t contain the letter S (that would have been too easy) and there had to be at least one pangram. For consistency, you were asked to use this word list (courtesy of computer scientist Peter Norvig) to check your game score.

The highest scoring honeycomb had an R in the center, with the letters AEGINT around it. This arrangement scored a whopping 3,898 points. If you don’t believe me, here’s a visualization showing each word in the honeycomb, with the letters in each word highlighted in pink:

There are some particularly high-scoring words contained in this honeycomb, like REAGGREGATING and REINTEGRATING (each worth 20 points).

As if finding this highest-scoring honeycomb wasn’t challenging enough, several members of Riddler Nation set out to write increasingly efficient algorithms for solving this puzzle.

At first, you might think there are countless letter combinations that you (that is, your computer) would have to sift through to find the best honeycomb. Out of 25 letters (remember, we excluded the S), there are more than 3 million possible ways to pick a central letter and then six other letters around it. Yikes! Solver Tyler Barron estimated that it would have taken his computer 584 days to crank through all those letter combinations.

But Peter Ji, our winner, didn’t try all 3 million honeycombs. He narrowed his search to letters that showed up most frequently in the word list. This approach didn’t *guarantee* the right answer, but it worked.

Meanwhile, solver Laurent Lessard definitively proved this was the best honeycomb by taking advantage of the fact that there had to be a pangram — that is, a word with exactly seven unique letters. In the given word list, there were only 14,741 pangrams, which corresponded to 55,902 possible honeycombs. It’s still a pretty big number, but it’s way smaller than 3 million. Along the way, Laurent also found the highest scoring honeycomb that *did *include an S (with an E in the center and AINRST around it, worth a cool 8,681 points) and the lowest scoring honeycomb (with an X in the center and CINOPR around it, worth a pathetic 14 points). Solver David Robinson wrote about a similar approach that also leveraged matrix operations.

Finally, Peter Norvig (the provider of the word list!) documented his incredibly efficient approach. By looking at the possible subsets of letters within a honeycomb, the final version of his program found the right answer in 2 seconds. Wow!

Solver Hector Pefo suggested that The New York Times use this highest-scoring honeycomb for the April Fools’ Day edition of Spelling Bee. It would surely drive the Spelling Bee community (also known as the #HiveMind) bonkers. How awesome would that be?

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!

Email Zach Wissner-Gross at riddlercolumn@gmail.com.

]]>Today’s number is 14.82 million, the number of people who tuned in to watch the first night of “Jeopardy: The Greatest of All Time” tournament on Wednesday. Champions Ken Jennings, Brad Rutter and James Holzhauer are scheduled to conclude the three-game tournament tonight at 8 p.m.

Even small increases in earnings can have huge health outcomes. A study published in the Journal of Epidemiology & Community Health this week found that states that raised their minimum wages by $1, reduced the suicide rates by 3.4 percent to 5.9 percent among adults between the ages of 18 and 64, whose highest educational attainment was a high school diploma or less. Researchers analyzed 25 years of monthly data from all 50 states and the District of Columbia. [Washington Post]

A new study from the National Center for Health Statistics shows drinking is rising in popularity among more Americans, resulting in more alcohol-related deaths. Researchers looked at almost 20 years of data and found nearly 73,000 people died in the U.S because of liver disease and other alcohol-related illnesses in 2017, more than twice as many people who died from the same health reasons in 1999. Researchers found that some of the greatest increases were among women and those who were 50 and older. [National Public Radio]

Chris Paul’s performance with the Oklahoma City Thunder this season has been so remarkable, FiveThirtyEight’s Chris Herring says he might “legitimately be the NBA’s best closer.” Through his scoring help, the team had won 10 of out of their last 12 games going into Thursday’s match against the Houston Rockets, and as Herring noted they are now tied for the second-most wins in the league. Paul’s ability to score in the fourth quarter has set him apart from the rest of the league, with his total of 103 points in the clutch as of Thursday afternoon, 20 more than Zach LaVine, the next closest player. [FiveThirtyEight]

The Russian Academy of Sciences appointed a commission to investigate unethical publication practices in an industry that has been known for low standards and thousands of cases of plagiarism as well as “questionable authorship,” according to Science Magazine, and now more than 800 papers from various Russian journals will be retracted. One former staffer at the U.S. National Science Foundation called the preliminary report from the RAS “a bombshell” for documenting the breadth of the problem. [Science]

On Thursday, Mexican environmental authorities announced that a red tide algae bloom was responsible for the deaths of 292 sea turtles from the country’s southern Pacific coast. The toxic algae had caused many of the turtles to stop breathing or keep their heads up. Volunteers, researchers and other authorities were able to save 27 of the Pacific Green sea turtles, though. [Associated Press]

**Educational debt is usually something that can’t be included when filing bankruptcy,** but one case might soon help more people drowning in student loans. Judge Cecelia G. Morris of the U.S. Bankruptcy Court in Poughkeepsie, N.Y., ruled that a U.S. Navy veteran didn’t have to pay $220,000 in student loan debt because “satisfying his law school debt in full would impose an undue hardship.” [Wall Street Journal]

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After a magnitude 6.4 earthquake struck Puerto Rico on Tuesday, the country is still struggling to restore power to the island. About one million people still had no power of Wednesday, partly because the island’s major power plant Costa Sur power plant, was seriously damaged in the quake. Thousands of people have slept outside their homes due to concerns further tremors could cause other buildings to collapse. [New York Times]

The World Health Organization says more than 6,000 people have died from a measles epidemic in the Democratic Republic of Congo, and there have been approximately 310,000 suspected measles cases reported since the beginning of last year. BBC News reports an emergency vaccination program was launched by the Congolese government and WHO last September, but the epidemic is currently the world’s largest. More than 18 million children under the age of 5 have been vaccinated, but the WHO says it would cost an extra $40 million to also vaccinate Congolese children between the ages of six and 14 to strengthen response to the out break. [BBC News]

Of the 176 passengers and crew who died in the crash of Flight PS752, which left Iran early Wednesday morning, 63 people were Canadians and almost half of them were from the city of Edmonton. A large number of the Canadian victims were doctors, scientists, researchers, and graduate students. The Ukraine International Airlines flight was on its way to Kyiv when it crashed only a few minutes after taking off from Tehran’s main airport. [CBC News]

The ecological damage of the Australian bushfires in Victoria and New South Wales is now estimated to be at least 800 million animals, as well as “hundreds of billions of insects.” The Sydney Morning Herald reports more than 6 million hectares have been destroyed so far, “including rainforest normally considered too wet to burn.” The damage is so extensive that “at least one species is feared extinct.” [The Sydney Morning Herald]

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IKEA, the popular Swedish furniture company, will pay $46 million to a California couple whose two-year-old son died from his injuries from a Malm dresser that tipped over and crushed him. In a statement, the couple’s lawyers said the financial amount from IKEA “is the largest wrongful death settlement related to one child in U.S. history.” In 2016, IKEA settled with families of three other children who were killed by the same line of dressers for a total of $50 million. [CNN Business]

At least 32 people are dead and dozens more have been wounded during a stampede at the funeral for Qassem Soleimani, one of Iran’s most powerful military leaders, who was killed last week in a targeted airstrike attack by the U.S. Iranian television said the stampede happened in Soleimani’s hometown, where he is to be buried. [National Public Radio]

You’re not supposed to get better with age as a defenseman in pro hockey, but John Carlson is proving to be a great exception to the rule. Even though the Washington Capitals player is turning 30 this week, Carlson is currently his team’s leader in scoring with 52 points (13 goals, 39 assists). FiveThirtyEight’s Terrence Doyle and Neil Payne also note that Carlson is so good, he’s “currently enjoying the ninth-best defenseman scoring season since 1943.” [FiveThirtyEight]

If you’ve ever wondered if the woman or nonwhite person you saw in an advertisement or on a dating app was real, artificial intelligence start-ups might make it much harder to figure that out. The Washington Post reports companies like the design firm Icons8 are now selling digital images of computer-generated faces that “look like the real thing” to marketing companies and dating apps. The sales pitch of the AI software is how it can quickly generate 1 million images in a single day, allowing companies to “increase diversity” without the costly process of finding real people. [Washington Post]

There were a lot of great movies that highlighted a female perspective or represented the diverse demographics of the United States, but you wouldn’t know it looking at who is nominated in the 2020 BAFTA film awards. This year, all of the 20 main acting nominations went to white actors and no women were nominated for best director. Marc Samuelson, chair of BAFTA’s film committee, told Variety, “It’s just a frustration that the industry is not moving as fast as certainly the whole BAFTA team would like it to be.” [TIME]

Many rare languages are at risk of disappearing, and Seke, which is spoken in just five villages in Nepal has only approximately 700 speakers left in the world, according to a recent study by the Endangered Language Alliance. The organization estimates there are roughly 100 Seke-speakers living in New York, and 50 of them live in one building in Flatbush, Brooklyn. One of the youngest residents there, Rasmina Gurung, has several relatives in the building, and is helping the Endangered Language Alliance compile a Seke-English dictionary. “I feel so much pressure,” she told the New York Times. “I need to get as much knowledge as possible. And fast.” [New York Times]

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LSU quarterback Joe Burrow has had a pretty remarkable turnaround, becoming what FiveThirtyEight’s Josh Planos describes as a “potential future No. 1 draft pick.” Burrow has nabbed 8 out of the 65 best single-game QBR performances this season. And during last weekend’s Chick-fil-A Peach Bowl, Burrow passed for 493 yards and scored eight touchdowns, an unprecedented accomplishment. His other stats include throwing 5,208 yards, 55 touchdowns, and completing more than 77 percent of his throws, which Planos notes puts Burrow on track to break the all-time record. [FiveThirtyEight]

A 5.8-magnitude earthquake happened on the American territory of Puerto Rico shortly before the sun rose on Monday, causing landslides, power outages as well as damage to at least 34 homes. Several more tremors followed in the hours after the initial quake, including a 5.0-magnitude one. The Associated Press says power lines were shaken and five of the damaged homes had collapsed, but no casualties or injuries have been reported. [Associated Press]

The editorial staff of Sports Illustrated announced their plan to form a union on Monday after the legacy magazine saw drastic layoffs in October following the acquisition of the magazine by Maven, a Seattle-based tech and media company. Roughly 80 staffers in print, digital and video are represented by the union. [CNN]

A new report from the National Bureau of Economic Research says the cost of President Trump’s trade war has been paid almost entirely by American businesses and consumers, not China. Experts and economists from the Federal Reserve Bank of New York, Columbia University and Princeton said analysis of tax levies found “approximately 100 percent” of import taxes fell on Americans, despite the president’s assertion the country was “taxing the hell out of China.” Some of the implemented tariffs on Chinese goods are as high as 25 percent. [New York Times]

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The heat from wildfires across southeastern Australia is so intense that clouds are raining down fire, not water. There are approximately 161 fires raging across New South Wales and Victoria. Temperatures have exceeded 100 degrees Fahrenheit and the blazes have already destroyed more than 22,000 square miles. [Wall Street Journal]

A massive crash involving two tractor trailers, a tour bus and several other vehicles has left at least five people dead and approximately 60 people sent to local hospitals. The crash, which happened early Sunday morning on the Pennsylvania Turnpike around 3:30 a.m., shut down 86 miles of the highway in both directions. Stephen Limani, a spokesperson from the Pennsylvania State Police, told USA Today, “It was kind of a chain-reaction crash” after the tour bus was struck by two tractor-trailers, followed by a collision with another truck and a passenger vehicle. [USA Today]

During the opening weekend of the NFL playoffs, the New England Patriots were dispatched by the Tennessee Titans, 20-13, bringing an end to an incredible era of post-season dominance. It is “their earliest elimination from the NFL playoffs since 2009” and dashed quarterback Tom Brady hopes for a seventh Super Bowl with the team. The 42-year-old quarterback has said he will not retire, but there are lingering questions about whether he will play with the Patriots next season or join another team. [NBC News]

Demand for theater is certainly alive in Chicago. A touring production of Lin-Manuel Miranda’s show “Hamilton” ended there this weekend after generating $400 million in sales over its three year stint in the city, making it one of the most financially successful shows in the city’s history. The Chicago Tribune reports the production sold “most of its weekend center orchestra seats for premium prices,” there were very few unsold seats, and “it spent very little on advertising, only mounting a significant marketing campaign in its final year.” [Chicago Tribune]

The health commission in Wuhan, a major city in Central China, says a viral pneumonia outbreak that has affected 59 people as of Sunday is not connected to the the flu-like and highly contagious Sars virus. Sars, which stands for severe acute respiratory syndrome, was responsible for the deaths of 349 people in mainland China, as well as 299 people in Hong Kong in 2003. The comments from the health commission were in response to false information published online speculating about the medical cases possibly indicating a resurgence of the virus. [AFP]

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From Jason Zimba comes a sequence of scrambled screens:

Each of the images below is a different nation’s flag in which the pixels have been randomly rearranged. Can you figure out which flag is which?

*Important note:* Some browsers can distort the colors of the flags. If you’d like to scrutinize these images, consider downloading them first, which you can do by right-clicking each image.

There will be one winner per flag. And if you’re a little rusty on your flags, you can view them all here.

**Flag A**

**Flag B**

**Flag C**

The New York Times recently launched some new word puzzles, one of which is Spelling Bee. In this game, seven letters are arranged in a honeycomb lattice, with one letter in the center. Here’s the lattice from December 24, 2019:

The goal is to identify as many words that meet the following criteria:

- The word must be at least four letters long.
- The word must include the central letter.
- The word cannot include any letter beyond the seven given letters.

Note that letters can be repeated. For example, the words GAME and AMALGAM are both acceptable words. Four-letter words are worth 1 point each, while five-letter words are worth 5 points, six-letter words are worth 6 points, seven-letter words are worth 7 points, etc. Words that use *all* of the seven letters in the honeycomb are known as “pangrams” and earn 7 bonus points (in addition to the points for the length of the word). So in the above example, MEGAPLEX is worth 15 points.

Which seven-letter honeycomb results in the highest possible game score? To be a valid choice of seven letters, no letter can be repeated, it must not contain the letter S (that would be too easy) and there must be at least one pangram.

For consistency, please use this word list to check your game score.^{5}

Congratulations to Josiah Jenkins of Rugby, North Dakota, winner of the most recent Riddler Express.

Last week, your office voted on a theme for its holiday party. It fell on you to record the percent of your coworkers (including yourself) who voted for each one. Since you were in a hurry, you just wrote down everything in the percentage that came before the decimal point. So for example, 35.0 percent, 35.17 percent and 35.92 percent would all be written simply as “35 percent.”

After the votes were tallied, you found that the winner received 73 percent of the vote (at least, that’s what you wrote down), while second place had 58 percent and third place had 32 percent. Apparently, people voted more than once. Based on these percentages, what was the minimum number of people who could work in your office?

Some solvers noted that in order to calculate the percentages in the first place, you must have known how many people worked in the office. That’s a fair point. But it’s the holidays, let’s be generous, people.

So let’s assume someone else told you the percentages; you can use them to figure out how many coworkers you have. One way to do this is to try out lots of different numbers. For example, there couldn’t have been 10 people in your office, since the only possible voting percentages would have been 0 percent, 10 percent, 20 percent, 30 percent, and so on up to 100 percent — 73, 58 and 32 percent would not have been possible. Meanwhile, there could have been 100 people in your office — then 73 people, 58 people and 32 people would have voted for the respective party themes. After this, it was a matter of trial and error to pin down the minimum possible number of people in the office. Many solvers, like Quoc Tran, wrote computer code to check which numbers worked and which didn’t.

Solver Tim Guindon constructed a Desmos graph that revealed the answer. Tim’s approach turned the information from the problem into equations. For example, if there were *N* people in your office, what did it mean that you wrote down 73 percent? It meant that there was some number of people *A* who voted for one of the choices, such that *A*/*N* was a percentage equal to 73 point something. Mathematically speaking, that translated to the following equation: floor(100·*A*/*N*) = 73. (If the floor function is new to you, worry not. It does exactly what you’d do in recording the percentage — it gets rid of everything after the decimal point.) Tim then went a step further, narrowing down which values of *A* he should check depending on the value of *N*. The end result was that there were at least **34 people** in the office. Had there been exactly 34 people, 25 people made up 73.53 percent, 20 people made up 58.82 percent and 11 people made up 32.35 percent. This was the smallest value of *N* that could have produced percentages that start with 73, 58 and 32.

For extra credit, you were asked to find the greatest number of people who *couldn’t *have worked in your office. We said earlier that there could have been 100 people in your office. Sure enough, any number *beyond* 100 was also possible, as proven by solver Mitch Schmidt. This is because the spacing between the possible percentages gets smaller and smaller, until you reach a point where there will always be percentages that start with 73, 58 and 32. Starting with *N* = 100 and working his way down, Mitch found that the biggest number of officemates that *didn’t *work was **88**. Had there been 88 people in the office, 51 people would have made up 57.95 percent, while 52 people made up 59.09 percent. There’s simply no way you could have recorded 58 percent.

Anyway, with that riddle behind us, here’s hoping your office’s holiday party fared better than the typical office party.

Congratulations to Hector Pefo of San Francisco, California, winner of the most recent Riddler Classic.

Last week, I had 10 pairs of socks in a drawer. Each pair was distinct from another and consisted of two matching socks. Alas, I was negligent when it came to folding my laundry, so the socks were not folded into pairs. Fumbling around in the dark, I pulled the socks out of the drawer, randomly and one at a time, until I had a matching pair of socks among the ones I had removed from the drawer. On average, how many socks would I have had to pull out of the drawer in order to get my first matching pair?

We can attack this problem one case at a time, as solver Jess Bianchi did, starting with the first sock. What’s the probability that I’d have a pair after I pull out the first sock? Well, one sock can’t possibly make a pair, so the probability is zero. On to the next case!

What’s the probability that I’d have a pair when I pull out my second sock? The first sock could have been any of the 10 pairs — but whatever pair it belonged to, of the 19 socks remaining in the drawer, only one of them pairs up with the first sock I pulled. That means my chances of making a pair on the second sock were 1/19.

And what about the third sock? To have my first pair upon pulling out the third sock, the second sock must *not* have made a pair. Since we just found the second sock makes a pair 1/19 of the time, that means it won’t make a pair the remaining 18/19 of the time. Once I’m pulling out that third sock, there are 18 socks remaining in the drawer, and exactly two of them will give me a pair (one that matches the first sock I pulled out, and one that matches the second sock I pulled out), meaning the probability is 2/18. Overall, my chances of getting my first pair with the third sock are then 18/19 · 2/18.

At this point, many solvers saw a pattern emerge. Continuing with the logic above, the probability of getting your first pair with the fourth sock were 18/19 · 16/18 · 3/17, and the chances for the fifth sock were 18/19 · 16/18 · 14/17 · 4/16. With each additional sock, the probability calculations included one more fraction to multiply, whose denominator decreased by one (because there was one less sock in the drawer) and whose numerator decreased by two (one for the sock that was removed and one for its paired sock you can’t pull in order to avoid having a pair). As you’d expect, these probabilities all add up to one upon reaching the eleventh sock, since at that point you’re guaranteed to have a pair by the pigeonhole principle.

To find the average number of socks needed for a pair, you can add up the products of each of these probabilities multiplied by their corresponding number of socks. The average number of socks needed for a pair turns out to be about **5.675** (the exact value is 262,144 divided by 46,189).

But for this puzzle, this solution was just the tip of the iceberg. The extra credit asked for a general solution when there were *N* pairs of socks instead of just 10 pairs. To the surprise of many, the answer was surprisingly compact. As *N* gets bigger, the average number of socks needed for a pair approaches √(𝜋*N*). This approximation worked pretty well for small values of *N* — for 10 pairs of socks, it gave you a reasonable value of 5.605 — and it got even more accurate as *N* got bigger.

At this point, you may be wondering how on earth a 𝜋 showed up in the solution (considering there weren’t any circles involved!). The constant 𝜋 can often appear in problems involving infinite sums and, on occasion, in approximating ratios of factorials of large numbers. Proving this result is beyond the scope of this column, but I will refer interested readers to the write-ups of Laurent Lessard, this week’s winner Hector and Emma Knight (who nicely explained why the answer should be proportional to the square root of *N*).

Still don’t believe me? Well here’s a graph showing how the exact solution compares with N for different values of *N*, courtesy of Laurent. I mean, just look how close those dots are to the curve!

If there’s a takeaway from all this, it’s that you shouldn’t lose sleep over all your unpaired socks. Pulling them all out of your drawer may be a lot of work, but finding a pair is then only the square root of a lot of work (times the square root of 𝜋).

Email Zach Wissner-Gross at riddlercolumn@gmail.com.

]]>The number of women holding the reins to the 100 top-grossing movies of the year was at its highest level in 2019 since at least 2007, though women — and particularly women of color — are still significantly underrepresented as directors. According to a study released Thursday from the USC Annenberg Inclusion Initiative, 12 of the 113 directors last year were women (10.6 percent), and four were nonwhite women (3.5 percent) — both high-water marks. But in the 13 total years of the initiative’s study, only 4.8 percent of the 1,300 movies analyzed were directed by women, and less than 1 percent of all directing jobs went to nonwhite women. [The Los Angeles Times]

Major League Baseball announced on Thursday that New York Yankees pitcher Domingo Germán had been suspended for 81 games under the sport’s domestic violence policy for an incident in September involving his girlfriend. The 27-year-old player will miss 63 games in the 2020 season; the suspension retroactively includes the nine regular-season and nine postseason games Germán missed while on administrative leave last year. He will not appeal the decision. [USA Today]

Prices for hundreds of pharmaceuticals went up on New Year’s Day, though the increase was actually smaller than that of a year ago. Data analysis from software company Rx Savings Solutions found that more than 60 drugmakers increased their prices on Wednesday by an average of 5.8 percent, following last year’s increase of 6.3 percent. Pfizer Inc. saw the largest average increase this year, raising prices by more than 9 percent on dozens of products. [The Wall Street Journal]

India often faces summer heat waves, but unseasonably cold weather is afflicting the northern part of the country this winter. On Monday, New Delhi broke a 119-year-old record for December when the maximum temperature reached just 49 degrees Fahrenheit — about 20 degrees lower than average, according to The New York Times. Air pollution levels are high because of the fog and stagnant winds, while a lack of centralized heating has resulted in school closures and hospitals flooded with patients suffering from pneumonia, coughs and colds. [The New York Times]

Severe flooding this week in Greater Jakarta has killed at least 26 people and forced more than 30,000 to evacuate. Heavy rains fell Tuesday and Wednesday across the flood-prone Indonesian capital, causing landslides and stranding some residents. Public transportation throughout Jakarta has also been affected. [The Jakarta Post]

If you’re thinking about cutting out or reducing booze as part of your New Year’s resolution, you’re far from alone — and major beer companies have more products aimed at your goal. In 2018, there was a 1.6 percent decline in beer consumption, with consumers reducing their overall intake or shifting toward cider and hard seltzer. Companies like Heineken and Molson Coors have launched no- or low-alcohol beers to jump on that trend and are promoting them this month as part of Dry January. [CNBC]

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The bushfires in Southwestern Australia are stunning in their devastation. The fires, which started in late August, have consumed more than 5 million hectares (or more than 12 million acres), killed nine people and destroyed about 1,000 homes. Incredibly, 500 million animals are thought to have been lost in the fires, including 30 percent of the country’s koala population. Australia’s fire season is typically at its most intense in January and February. [Scientific American]

Teachers who reflect the diversity of their students can significantly increase attendance and participation among those students and can even motivate college applications. But for many Latino children in America, a teacher who looks like them is a statistical rarity. After analyzing the data from school districts in 46 states as well as the District of Columbia, The Washington Post found that only 0.1 percent of Latino students “attend a school system where the portion of Latino teachers equals or exceeds the percentage of Latino students.” [The Washington Post]

If your New Year’s resolution is to join a sport, take inspiration from the growing number of American girls who are starting and joining female-specific wrestling teams. The Wall Street Journal reports that interest and participation have risen after more states launched wrestling championships specifically for girls, with Missouri experiencing a turnout eight times higher than the year before. While that state’s surge was notable, the National Federation of State High School Associations says it’s part of a much larger trend: Last season, there was a 28 percent increase in participation in girls wrestling across the country. [The Wall Street Journal]

At least 30 animals were killed at the Krefeld Zoo in northwestern Germany after a fire tore through a monkey enclosure early on New Year’s Day. The zoo’s director, Wolfgang Dressen, said victims of the fire included “highly endangered monkeys like orangutans from Borneo, lowland gorillas from Central Africa and chimpanzees from West Africa.” The official cause of the fire had not yet been confirmed late Wednesday. [CNN]

The NFL instituted a rule 16 years ago requiring teams to interview at least one nonwhite candidate for any available head coaching gig. But the 2019 NFL Racial and Gender Report Card says the league hasn’t performed this poorly on its racial hiring practices since it started collecting this data in 2004, and only three black men are currently employed as head coaches. Troy Vincent, a former player and the NFL’s current executive vice president of football operations, was pretty blunt about the league’s grade: “When you look at the demographics, it’s embarrassing.” [The New York Times]

It’s hard to believe how much of an impact Pokemon Go had on the world in the summer of 2016, instantly drawing millions of users and changing the way people interacted with augmented reality through video games and cellphone apps. But a new report from CBC News based on 471 pages of internal files shows just how much the popular game caught Canada’s military off guard. Civilians had to be officially warned to stay off military property, despite the presence of popular PokeGyms and PokeStops. [CBC News]

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So we decided imitation is the sincerest form of flattery. Here are the stories other folks published in 2019 that made the FiveThirtyEight staff turn a bit green.

*By Sahil Chinoy, The New York Times*

Chinoy’s visual and interactive exploration of the characteristics that can predict someone’s political party affiliation is not only engaging and visually striking, but also insightful about the factors driving divisions in American politics. Users can answer yes-or-no questions about themselves to see how strongly these characteristics change their predicted party affiliation, then explore how the country as a whole answered the same questions. This approach visualizes how identity-driven politics have widened our political divides.

*— Ryan Best, visual journalist*

*By Josh Katz and Kevin Quealy, The New York Times*

One thing we at FiveThirtyEight love to think about — and sometimes struggle to do — is how to show uncertainty in our data. This subway variability calculator is fun to play with, but it also does a great job showing how and why the variability of an estimate (in this case, your commute time) matters.

*— Laura Bronner, quantitative editor*

*By Maryn McKenna, The New Republic*

This piece tying together politics and public health is a masterful exploration of how nationalist movements, suspicion of expertise, and anti-immigrant fervor can impact things like vaccination campaigns and efforts to stop ebola outbreaks.

*— Maggie Koerth, senior science writer*

*By Foolish Baseball*

One of my favorite baseball storytellers of the year is a YouTuber who goes by Foolish Baseball. In 2019 he began to regularly post videos about a bunch of different sabermetric topics: Larry Walker’s Hall of Fame case, the theory that Ichiro could hit home runs if he wanted to, Albert Pujols’s incredible slowness and Juan Soto’s ridiculous early-career numbers. But I think my favorite might be this one, about Pedro Martínez’s 1999 and 2000 seasons, which each might be the best in MLB history. It’s been fun to watch someone merge data and analysis with the medium of YouTube, and I’m looking forward to seeing what he does — in his distinctive 8-bit style — in 2020.

*— Neil Paine, senior sportswriter*

*By Steve Kornacki, NBC News*

With a little over a month to go before the Iowa caucuses and the primary race still very much in flux, here’s an important stat to keep in mind: Since 1992, no Democratic candidate has won the presidential nomination without also winning a majority of the black vote. In July, Steve Kornacki and NBC News dug deep into the archives to assemble the first publicly available data set of how black Americans have voted in each of the nine competitive national Democratic campaigns since 1976, and as you can read for yourself in the 10-part series, the importance of African Americans in the Democratic primary cannot be overestimated. In 2016, black voters made up nearly a quarter of the Democratic primary electorate and they could make up an even larger percentage in 2020, so chances are they’ll be crucial once again in deciding the party’s nominee.

*— Sarah Frostenson, politics editor*

*By Robert Gebeloff, The New York Times*

Urban vs. suburban vs. rural has become one of the most important divides in politics, yet it’s surprisingly hard to measure a place’s density. Robert Gebeloff at the New York Times’ The Upshot made a big contribution to this in October by assigning individual census tracts a neighborhood density score from 1 to 10. It’s a great complement to CityLab’s Congressional Density Index from 2018 — less comprehensive, but more granular.

* — Nathaniel Rakich, elections analyst*

*By Astead W. Herndon, The New York Times*

This is not a data story. But it clearly showed a knowledge of the data on black voting patterns. And it showed a real depth in writing about black voters (note that Herndon refers to Biden being supported by more moderate and older black people, not just black people) and racial issues (he captured why being black was not enough to voters who were looking for more).

*— Perry Bacon Jr., senior politics writer*

*By Dean Halford, Lauren Leatherby, David Ingold and Justin Bachman, Bloomberg*

The Bloomberg Graphics team used sharp visual animation to show where all Boeing 737 Max jets across the United States went after they were grounded back in March. This piece also offers insight into how airlines dealt with the grounding of these jets, which Boeing will stop producing in January.

*— Ryan Best, visual journalist*

*By Philip Bump, The Washington Post*

We’ve written a few times about how President Trump has had more Cabinet turnover than any modern president — and in so doing, I noticed that Trump has had an awful lot of “acting” Cabinet members. But before I could do the historical research to write about it, Philip Bump of The Washington Post had already done so. As of April, Trump was employing acting Cabinet members at a much faster rate than any of his recent predecessors.

*— Nathaniel Rakich, elections analyst*

*By Allison McCann, The New York Times*

The Women’s World Cup happened last summer and the U.S. Women’s National Team dominated, breaking all kinds of records. Near the start of the tournament, former FiveThirtyEighter Allison McCann had this piece in The New York Times that made me very jealous. The Times had sent a survey to the teams participating in this year’s World Cup and had given players cameras to document their lives. The end product was wonderful and poignant.

*— Meena Ganesan, social editor*

*By Kim McCauley, SBNation*

Back in early October, this tweet took over soccer Twitter for half a day:

We couldn’t stop thinking about Elizabeth Warren as a striker, Joe Biden as a fullback or how this particular field fits in a 4-3-3 formation. This is the kind of debate FiveThirtyEight should be a part of, in my humble opinion, which is why I was so jealous when Kim McCauley was able to jump on this topic so quickly and publish a breakdown of the formation and how each candidate would perform in his/her position. It was perfect.

*— Tony Chow, video producer*

*By Eliza Shapiro and K.K. Rebecca Lai, The New York Times*

This deep dive into the changing racial composition in New York’s specialized public high schools is fascinating and thorough; one thing that struck me in particular is how well it contextualizes the changes in specialized schools by comparing them to the share of all students in the city’s school system.

*— Laura Bronner, quantitative editor*

*By Emily Badger, The New York Times*

What’s not to love about this playful story from Emily Badger of The New York Times, which explores the challenges and opportunities of urban planning in the developing world through the eyes of Paul Romer, an economist looking for lessons in the “instant city” that emerges every year at the famous festival in the Nevada desert? It’s a fresh and compelling exploration of a knotty (and nerdy) policy topic — something that’s certainly not easy to pull off.

*— Amelia Thomson-DeVeaux, politics writer*

*By Meredith Wills, The Athletic*

Astrophysicist and baseball enthusiast Meredith Wills deconstructed baseballs down to their cores to try to understand what role the ball was playing in the game’s home run surge. What she found was something of a smoking gun: The ball is much different, from the smoothness of the leather to the length of material used in seams.

*— Travis Sawchik, sportswriter*

*By **Nate Cohn**, The New York Times*

I wish I’d written this piece because it synthesizes some points I’ve made in a couple articles so far this year, such as how representative the Super Tuesday states are of the Democratic primary electorate as a whole. It also digs into the shifts in the delegate calendar compared to 2016 and has some nice charts!

*— Geoffrey Skelley, elections analyst*

*By Jonah M. Kessel and Hiroko Tabuchi*

I love this recent New York Times story that used a specialized camera to spot otherwise-invisible methane leaks at oil refineries. Such a cool use of technology in the service of exposing a hidden side of the climate problem.

*— Maggie Koerth, senior science writer*

*By Sarah Almukhtar, Blacki Migliozzi, John Schwartz and Josh Williams, The New York Times*

I’m not just jealous of this composite look at flooding in the U.S. in 2019 because of its blend of mapping, reporting and imagery, though all that compellingly reveals the scope of an environmental disaster that, since it takes place in many locations at different times, might otherwise be difficult to demonstrate. I’m also jealous of the sheer ambition and amount of work that must have gone into it — to take on a complex issue and find the best possible way to show a full picture of it regardless of the challenge is what great visual journalism should aspire to be.

*— Ella Koeze, visual journalist*

- “Just because Republicans aren’t winning in cities doesn’t mean that no Republicans live there,” Rachael Dottle wrote earlier this year. Using historical vote data, she showed where every city’s Republican enclaves were, and which cities were the most politically segregated.

- Clare Malone went home to Cleveland’s suburbs to examine how the 2016 election laid bare political differences among white Americans. Clare found that the fissures had been lying in wait for decades.
- How do you measure a gerrymandered district? Ella Koeze and William Adler showed how math can help expose which districts have been manipulated along partisan lines.

- Black politicians on the local level live different political lives than black politicians who want to be president. In August, Perry Bacon Jr. dug into why that is.
- Activists who want to restrict access to abortion made some progress on the state level this year. Amelia Thomson-DeVeaux categorized hundreds of abortion restrictions to show why the anti-abortion movement is escalating.
- Automatic voter registration is a recent hobbyhorse of progressive activists. But is it the panacea it’s made out to be? Nathaniel Rakich looked at what happened when 2.2 million people were automatically registered to vote.

- We’re told over and over again that politicians need to appeal to centrist moderates if they hope to win nationally. But Lee Drutman’s analysis suggests that narrative isn’t true. The moderate middle is a myth.
- Clare Malone spent weeks tailing former Vice President Joe Biden to understand a contradiction at the center of his presidential campaign: black voters provide a lot of his support, but one of his biggest vulnerabilities is his record on race.

- Speaking of Biden, it can sometimes seem like it’s tough to dislodge a primary front-runner. But Geoffrey Skelley chronicled all the other front-runners who haven’t won. The list is long.
- Amelia Thomson-DeVeaux and Dan Cox wrote about one more way millennials are different than boomers: they’ve left religion behind, and they’re probably not coming back.
- In the very first House vote on impeachment, to simply formalize the process, Perry Bacon Jr. identified the political faultlines that would define the inquiry into the Ukraine scandal. Hint: They had to do with partisanship.
- Does it seem to you like President Trump’s job approval ratings hardly budge? Well, that’s true. But Geoffrey Skelley looked at how unusual Trump’s ratings are historically.
- The number of women in the Democratic field this cycle is unprecedented. And we don’t have any research on how sexism might affect such a race. But that doesn’t mean we know nothing about sexism’s electoral impact — Amelia Thomson-DeVeaux and Meredith Conroy put together a link-heavy introduction to what we know already, and how that could influence the 2020 primary.

- We try and find overlap between politics and sports wherever we can, but that doesn’t mean we’re always good at knowing which is which. Earlier this year Tony Chow quizzed us on whether color commentary happened after a game or after a Democratic primary debate.

- “Space Jam 2” is coming, and we’re hoping to be LeBron James’s casting director. We used our NBA metrics to cast the true successors to the cast of the original “Space Jam” movie.
- It’s always tough to measure how good a defender is in the NFL. But Michael Chiang figured out a clever new way: look at where opposing offenses
*aren’t*throwing.

- How many clichés are in your average college fight song? We tried to figure out the answer.
- Chris Herring attempted to solve one of the great mysteries of the NBA: “Why are there so many bats at Spurs games?”
- Another big mystery: How do you accurately evaluate college quarterbacks for the pro game? Josh Hermsmeyer looks at how the NFL does it (poorly), and offers some alternative solutions.

- Some people watch the Super Bowl for the football, and some people watch it for the halftime show. Gus Wezerek belongs to the latter, and he used data to rank 25 years of Super Bowl halftime shows.
- How national is your college football team’s fanbase? And why is a random county in South Dakota buying so many USC tickets?
- MLB commissioner Rob Manfred has been on a warpath against the parts of baseball he thinks are slowing down the game. Travis Sawchik found a culprit Manfred hasn’t targeted: foul balls.
- It’s still relatively early in the 2019-20 NBA season, but the pairing of LeBron James and Anthony Davis on the Los Angeles Lakers has been really good. Actually, Neil Paine found that it’s been historically great.
- We put Nate Silver in a dinosaur costume.

- Most personality quizzes on the internet are bunk. This one is backed by science.
- Conspiracy theories permeate our politics and culture. But get used to them. Maggie Koerth wrote that they can’t be stopped.
- We publish a lot of forecasts here at FiveThirtyEight. But are they any good? Jay Boice and Gus Wezerek collected virtually every forecast FiveThirtyEight has ever done to find out. The short answer: Yes, they’re pretty good.
- Christie Aschwanden had simple advice for those who work out: you don’t need sports drinks to stay hydrated.

You made it all the way here? We admire your commitment to great visual journalism! Check out our lists from 2018, 2016, 2015, and 2014.

]]>Where a kid grows up in America can have a huge effect on their long-term prospects — good schools, neighborhood safety, access to healthy food and places to play all play an important role. New data from the Institute for Child, Youth and Family Policy at Brandeis University reveals how access to these opportunities breaks down along racial lines in nearly every major metropolitan area in the U.S. In the Arbor Hill neighborhood in Albany, New York, for example, 97 percent of children are black or Hispanic; the area received a 1 out of 100 on the Child Opportunity Index, one of the lowest scores possible. [National Public Radio]

African swine fever is continuing to spread, with Indonesia the latest place in Asia to experience an outbreak. The virus has wiped out more than half of China’s herd this year. The BBC reports that, on Wednesday, Indonesia’s agriculture ministry said “nearly 30,000 pigs have died from the disease in North Sumatra.” Other affected countries include Vietnam, the Philippines, Mongolia, Cambodia, South Korea, North Korea, Myanmar and East Timor. [BBC News]

Residents in the New York City borough of Queens were told that the cause of a massive sewage backup that flooded 127 homes with raw sewage on Nov. 30 was someone pouring grease down the drain. They were right to doubt that explanation. The New York Times reports that the real culprit was a collapsed pipe. Many residents are still struggling to recover weeks later, and the City of New York might be liable for several million dollars in damage claims. [New York Times]

Facial recognition technology can be incredibly unreliable despite being widely used by law enforcement in the U.S. A landmark federal study released on Thursday found that Asian and African American people “were up to 100 times more likely to be misidentified than white men, depending on the particular algorithm and type of search,” The Washington Post reports. The study also found that Native Americans had the highest false-positive rate. [Washington Post]

The next leap in bathroom technology is here: A more uncomfortable toilet! StandardToilet, a British company, has filed a patent for a toilet with a seat that slopes down at 13 degrees, making it a pain to sit on for a long time. The idea here is that companies would put these toilets in workplaces, thus encouraging employees to take care of their business quickly and get back to work. [HuffPost]

Some good news from Mother Nature: a multi-decade effort to bring back a bird species from the brink of extinction has been successful enough to move the specifies from “extinct in the wild” to “critically endangered.” There are now at least 260 Guam rail roaming freely on two tropical islands. A long-term captive breeding program was behind the successful population increase, and researchers are hopeful the current number of birds is sustainable. [CNN]

*Significant Digits will be on break between December 23 and January 1. The key number during that period is the amount of quality time spent with family and friends. Thanks again for reading, sharing, and subscribing. Happy Holidays and Happy New Year from everyone at Team SigDig and FiveThirtyEight.*

From Mark Hannan comes a holiday party stumper:

You’re new at your job, and your office is voting on a theme for its holiday party. It’s fallen on you to record the percent of your coworkers (including yourself) who voted for each one. Well, since you’re in a hurry, you just write down everything in the percentage that comes before the decimal point. So for example, 35.0 percent, 35.17 percent and 35.92 percent would all be written simply as “35 percent.”

After the votes are tallied, you found that the winner received 73 percent of the vote (at least, that’s what you wrote down), while second place had 58 percent, and third place had 32 percent. Your first realization is that you work with a bunch of cheaters who voted more than once. But your second thought is that you might be able to use this information to figure out how many people work in your office. (As I said, you’re new, and this isn’t something you know off the top of your head.)

Based on these percentages, what’s the minimum number of people who could work in your office?

*Extra credit:* Your office could be filled with many possible numbers of people. Based on the percentages given in the problem, what’s the greatest number of people your office *can’t* have?

From Kathy Bischoping comes a question we’ve all asked ourselves at one time or another:

I have 10 pairs of socks in a drawer. Each pair is distinct from another and consists of two matching socks. Alas, I’m negligent when it comes to folding my laundry, and so the socks are not folded into pairs. This morning, fumbling around in the dark, I pull the socks out of the drawer, randomly and one at a time, until I have a matching pair of socks among the ones I’ve removed from the drawer.

*On average*, how many socks will I pull out of the drawer in order to get my first matching pair?

(Note: This is different from asking how many socks I must pull out of the drawer to *guarantee* that I have a matching pair. The answer to *that* question, by the pigeonhole principle, is 11 socks. This question is instead asking about the *average*.)

*Extra credit:* Instead of 10 pairs of socks, what if I have some large number *N* pairs of socks?

Congratulations to Carl Ollivier-Gooch of Vancouver, Canada, winner of last week’s Riddler Express.

Last week’s puzzle concerned a historic chess battle — the infamous 1984 World Chess Championship match between Anatoly Karpov and 21-year-old Garry Kasparov. The match was supposed to have been played until one of them had won six games. Instead, it lasted 48 games, of which Karpov won five and Kasparov won three, with the remaining 40 games ending in a draw. Alas, the match was controversially terminated without a winner.

If we assume Karpov’s chances of winning each game were 5/48, Kasparov’s chances were 3/48, and the chances of a draw were 40/48, what would have been Kasparov’s chances of eventually winning the match?

Many solvers broke the problem up into countless cases, depending on how many more games Karpov and Kasparov played until one of them had won six games — an approach that would indeed get you the right answer (eventually). But as Carl noted, the draws were actually “red herrings” that we needn’t worry about. They’d extend the match another game but had no effect on the overall winner. All that mattered were the games won by Karpov or Kasparov. Based on the given probabilities, Karpov was expected to win five games for every three won by Kasparov. In other words, in games with a winner, Karpov’s chances of winning were 5/8, and Kasparov’s chances were 3/8.

Now to figure out Kasparov’s chances of winning, we only wanted to know what happened in the next three games *that had a winner*. Those three games could have been the next three that were played, or they could have come after hundreds or even thousands of draws — it didn’t matter because the *draws* didn’t matter. At some point down the road, there would have to have been three games with a winner, since the probability that they’d continue to draw *forever* was zero.

Because Kasparov was down five games to three, and the winner was the first to have won six games, Kasparov needed to win all three of these games that had a winner. If he were to lose just one of them, Karpov would have reached six victories and won overall. We can find Kasparov’s chances of winning these three games by multiplying the independent probabilities: 3/8 × 3/8 × 3/8 = **27/512**, or about 5.3 percent. Not the best odds for Kasparov.

Some readers interpreted the question as asking for Kasparov’s chances of victory if the match had started over, with each player having won zero games apiece and the same probabilities of winning and drawing. Solvers Luca Alessi and Nick Charchut both found that Kasparov’s chances of winning from a clean slate would have been about 19 percent. Better for Kasparov, but still not great.

Nevertheless, when Karpov and Kasparov resumed play in the 1985 World Chess Championship, Kasparov emerged victorious!

Congratulations to Jimmy Wilkinson of Bethesda, Maryland, winner of last week’s Riddler Classic.

Last week, you were asked to find as many rectangular prisms (also known as cuboids) as you could whose volume (in cubic units) was the same as their surface area (in square units). You were also given a head start: A cuboid that’s 6 × 6 × 6 is one such solution, with a volume of 216 cubic units and a surface area of 216 square units. But what other cuboids satisfied this requirement?

Many solvers turned to their computers for help. For example, Ken Chambers wrote some code that tested cuboids whose dimensions were anywhere from 1 to 1,000. From all those possible combinations, there were only 10 whose volumes matched their areas:

Length | Width | Depth | Volume (cubic units) | Surface Area (square units) |
---|---|---|---|---|

3 | 7 | 42 | 882 | 882 |

3 | 8 | 24 | 576 | 576 |

3 | 9 | 18 | 486 | 486 |

3 | 10 | 15 | 450 | 450 |

3 | 12 | 12 | 432 | 432 |

4 | 5 | 20 | 400 | 400 |

4 | 6 | 12 | 288 | 288 |

4 | 8 | 8 | 256 | 256 |

5 | 5 | 10 | 250 | 250 |

6 | 6 | 6 | 216 | 216 |

Despite having tested some very large cuboids, each of these 10 that Ken found is pretty small in the grand scheme of things. The largest side length in this list is only 42 (of course). Surely there are other, larger solutions that our pitiful computers just weren’t powerful enough to find, right?

You might think so, but as solver Laurent Lessard showed, these were the *only* 10 solutions. We’re looking for whole number side lengths *a*, *b*, and *c* such that *abc* (the volume) equals 2*ab* + 2*bc* + 2*ac* (the surface area). That is, *abc* = 2*ab* + 2*bc* + 2*ac*. It’s safe to assume — “without loss of generality,” as mathematicians would say — that *a* ≥ *b* ≥ *c*. In other words, whichever of the three dimensions is longest, we’ll call that one *a* (and we’ll call the shortest one *c* and the middle one *b*).

Since *a* and *b* are the longest two sides, *ab* is at least as large as *bc* and *ac*. That means 2*ab* + 2*bc* + 2*ac* is at most 2*ab* + 2*ab* + 2*ab*, or 6*ab*. Putting our original equation and this inequality together, we have *abc* ≤ 6*ab*. Finally, dividing both sides by *ab* shows us that *c* ≤ 6. In other words, the shortest side of our cuboid must have length 1, 2, 3, 4, 5 or 6 — but not longer than 6! At this point, Laurent explored each of these six possible values for *c* on a case-by-case basis, finding the possible whole number values for *a* and *b*. (He does this rather elegantly by rearranging the equations as factor pairs.) Sure enough, there were **10** solutions.^{7}

Looking back at the 10 cuboids in the table above, solver Austin Shapiro further noticed that none of these cuboids will fit inside of another. I admit, neither of us quite understands the significance of this fact, but it *is* an interesting observation nonetheless.

Anyway, it turned out there were exactly two rectangles with matching area and perimeter: 3 × 6 and 4 × 4. And there were 10 rectangular prisms (i.e., three-dimensional rectangles) with matching volume and surface area. Some readers asked, “What about higher dimensions?” Sure enough, there’s a sequence for that! There are 108 four-dimensional cuboids with matching “surface area” and “volume” (of the four-dimensional variety, that is). There are also 2,892 five-dimensional cuboids with this property and 270,332 six-dimensional cuboids. However, no one knows precisely how many there are in seven or more dimensions.

Once again, we have come to the edge of human knowledge. Perhaps a clever and resolute member of Riddler Nation will be up to this seven-dimensional challenge …

Email Zach Wissner-Gross at riddlercolumn@gmail.com.

]]>The ability to defeat President Trump is still a top concern among Democratic primary voters, according to a new FiveThirtyEight/Ipsos poll: 64.2 percent of respondents said they preferred a candidate who has a good chance of beating Trump over a candidate who agrees with them on issues. And, on average, likely primary voters think Joe Biden — followed by Bernie Sanders and Elizabeth Warren — have the best chance of winning the general election. But we’ll see if tonight’s debate changes anything — the same group of respondents will be asked how they feel about all seven candidates again after the debate [FiveThirtyEight]

Only two women are given spots at P.D.C. World Darts Championships, but Fallon Sherrock certainly made the most of hers. On Tuesday, the 25-year-old became the first woman to defeat a man in the tournament. She sealed her win against Ted Evetts after successfully hitting a double 18. [New York Times]

An analysis of court records, sentencing memorandums and the newspaper’s own archives by the Baltimore Sun found at least 20 Baltimore police officers — some now no longer employed by the police department — were either charged with crimes, sentenced or suspended in 2019. [Baltimore Sun]

Two years ago, Shiori Ito went public with accusations of rape against a prominent TV journalist named Noriyuki Yamaguchi. On Wednesday, a district court in Tokyo not only dismissed Yamaguchi’s countersuit against Ito, but ordered him to pay her 3.3 million yen (approximately $30,000) in damages. Ito’s experience of speaking publicly and going to court with a civil suit made her a face of Japan’s #MeToo movement, but also subjected her to extensive amounts of abuse online. [The Guardian]

Many American cities are experiencing cold temperatures and “snow squalls,” but huge parts of Australia are facing a much different problem: record-high temperatures and massive wildfires. On Tuesday, the country experienced its hottest day ever recorded, reaching an average maximum temperature of 105.6 degrees Fahrenheit nationally. However, experts at the country’s Bureau of Meteorology think this record could be broken pretty soon because of intensifying heat expected on Wednesday. [National Public Radio]

Some thieves target jewelry; others desire crustaceans. A Boston man tried to steal $10,000 worth of freshly-caught lobster being loaded into a truck bound for Europe before crashing the vehicle into another truck. The failed robbery happened on Tuesday shortly after midnight. [Boston Magazine]

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The Mormon Church encourages its members to donate 10 percent of their income to the church, a practice known as tithing. But a former investment manager has submitted a whistleblower complaint to the Internal Revenue Service alleging that a tax-exempt investment fund tied to the Church of Jesus Christ of Latter-day Saints now has approximately $100 billion, “stockpiling their surplus donations instead of using them for charitable works,” as the Washington Post reports. The complaint also says the non-profit that amassed this money “has not directly funded any religious, educational or charitable activities in 22 years.” [Washington Post]

You might know that followers and fans of Andrew Yang, the Asian-American Democratic presidential candidate, are nicknamed the “Yang Gang.” Then again, if you don’t, that’s not surprising either — Yang’s support hovers only around 3-4 percent in national polls, on average.) But FiveThirtyEight’s Geoffrey Skelley highlights one area where Yang is leading: share of supporters who are under the age of 45. Yang’s number is 74 percent — that is, about 3-in-4 Yang supporters are 44 or younger and 1-in-4 are 45 or older. For comparison, Bernie Sanders is the only other candidate who’s base is at least half 44 or younger (69 percent). [FiveThirtyEight]

Training to run a marathon is hard. Competing at an elite level in the Boston Marathon is even harder. Qualifying for the Olympics in the marathon category is among the toughest things to do in running. But Des Linden is going to attempt to do all of that, even though the Boston Marathon and Olympic qualifiers are just 51 days apart. The 2018 Boston Marathon champion is planning to run the U.S. Olympic trials on Feb. 29 in Atlanta, then line up for the Boston Marathon on April 20. [Wall Street Journal]

A massive mussel die-off is happening in the Clinch River, in Tennessee, with significant declines in population and 10 species that have gone extinct. A few years ago, biologist Jordan Richard from the U.S. Fish and Wildlife Service found that pheasant shell mussels were dying at high rates; the population fell from 94,000 in 2016 to less than 14,000 this year — a decline of 85 percent — along a 200-meter (219-yard) stretch. [Associated Press]

A little black wad of ancient chewing gum can tell us a lot about what life was like 5,700 years ago. That’s what paleogeneticist Hannes Schroeder learned after a student brought him a lump of birch pitch from a Stone Age site in Denmark, and asked if they could get DNA out of it. Sequencing went so well, that “researchers were able to reconstruct a complete human genome,” NPR reports, and deduce several kinds of information abut the ancient woman who chewed the gum. [National Public Radio]

The holidays can be a tough, lonely time for many people and families who can’t afford to travel to see their loved ones. The families of incarcerated Americans face even steeper costs for phone calls, emails and basic supplies like soap due to high rates for communication services and commissary items. The Prison Policy Initiative estimates family and friends spend an additional $2.9 billion each year on basic items and phone calls. [New York Times]

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Fashion Nova is an incredibly popular fast-fashion brand — producing inexpensive clothes, very quickly, that are promoted mostly on social media by influencers and celebrities (there’s a collection designed by Cardi B). But a multi-year investigation by the federal Labor Department found Fashion Nova clothing being made in factories in Los Angeles that paid illegally low wages. Sewers were reportedly paid as little as $2.77 per hour. And internal federal documents showed those factories owed workers $3.8 million in back wages. [New York Times]

If you’re tempted to buy several items online with the intention of returning many of them, retailers have caught on, and they’re moving quickly to dissuade shoppers from the practice. Consumer returns in the United States ballooned to $369 billion in merchandise last year. That’s 10 percent of total retail sales. And many returned-but-then-unsold items go straight to landfills. Some companies are starting to charge fees for returns, only offering store credit and/or even blacklisting “repeat offenders.” [Bloomberg News]

Thousands of high school students have just received college acceptance notices, but the cost of that education can vary wildly from one state to another. An analysis of private and public tuition data from a financial technology company found several years of reduced state funding in Montana resulted in tuition going up by 8.6 percent for the same five-year period. On-campus room and board also skyrocketed by 18.16 percent more than inflation, the highest increase in the country. [Yahoo Money]

The Jacksonville Jaguars are in the news. (It may be the team’s most culturally relevant moment not having to do with “The Good Place.”) According to ESPN, an NFL arbiter has ruled that the team’s practice of fining players for missing medical and training sessions violated the league’s collective bargaining agreement. Those things are not allowed to be mandatory. The NFL players union (NFLPA) filed a grievance against the Jaguars, who docked one player — eventually revealed to be Dante Fowler Jr. — more than $700,000 in aggregate. The NFLPA letter also mentioned that more than 25 percent of the total grievances filed by NFL players have concerned Jacksonville, warning its members, “you as players may want to consider this when you have a chance to select your next club.” [ESPN]

LeBron James and fellow Los Angeles Laker Anthony Davis are currently on track to be one the most prolific and successful player pairs in NBA history. According to my colleague Neil Paine, James has already dropped 86 assists to Davis this season, “the most by any player to a teammate in the NBA so far, according to data from Second Spectrum.” [FiveThirtyEight]

Driving on two stretches of highway in Monterey County, California, requires extra caution: 62 vehicles have been struck by projectiles this year so far, prompting the launch of a task force and investigation. Capt. Kyle Foster of the California Highway Patrol told the Los Angeles Times that the incidents “began to pick up in frequency in early October, and investigators think they are linked.” [Los Angeles Times]

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A new report from the San Diego Tribune found that in the last year, after the Trump administration made “drastic changes” to U.S. asylum policy, only 11 people have been granted asylum in the Migrant Protection Protocols program, also known as Remain in Mexico. That’s only 0.1 percent of all completed cases. The policy changes have “effectively made the majority of non-Mexican migrants ineligible for asylum.” [San Diego Union Tribune]

Over the last 10 years, the Drug Enforcement Administration has made 179 arrests in reverse-sting cases in the Southern District of New York. However, a nonprofit legal defense group representing representing Johansi Lopez, who was arrested earlier this year in one of those stings, says that none of the people arrested in those cases have been white — all but two were black or Latino. The group Federal Defenders of New York is says Lopez’s arrest is “part of an alarming trend” within the DEA and other agencies that has produced racially biased results in both New York and other major American cities. [Washington Post]

With the next federal election fewer than 11 months away, a state judge in Wisconsin ordered the removal of up to 234,000 people from the registered voter list because they were flagged as having potentially moved. On Friday, Ozaukee County Judge Paul Malloy “sided with three voters represented by a conservative law firm who argued the state elections commission should have immediately deactivated any of the roughly 234,000 voters who didn’t respond to an October mailing within 30 days.” President Trump carried Wisconsin by fewer than 23,000 votes in 2016. Wisconsin residents can still register to vote as late as Election Day as long as they have photo ID and proof of their address. [PBS NewsHour]

The investigation into the deadly shooting last week at a kosher deli in Jersey City, New Jersey, carried out by David N. Anderson and Francine Graham is widening. When Anderson took part in the shooting, which killed four people, he had the phone number and address of a pawnshop almost 40 miles south of Jersey City in his back pocket. The New York Times reports on Ahmed A-Hady’s store and its connection to the anti-Semitic shooting. Ten guns and over 400 rounds of ammunition police were found inside the pawnshop on Friday. Early the next day, A-Hady was arrested on criminal weapons charges. [New York Times]

World War II may have ended many decades ago, but its weapons still have the capacity to uproot thousands of people. Roughly 53,000 residents of the southern Italian city of Brindisi were evacuated after a 440-pound, unexploded British bomb was discovered. The bomb, containing 40 kilograms of dynamite, was likely dropped on the city during an air raid in 1941. It was successfully defused. [The Telegraph]

Eva Gordon died last year at the age of 105, but the secret of her estate’s incredible generosity to community and technical colleges in Washington became public knowledge only recently. Seventeen educational institutions will split $10 million — approximately $550,000 each — with some of the funds specially designated for first-year student scholarships and financial aid for student housing. Gordon’s godson John Jacobs, a financial adviser for Morgan Stanley in Seattle, told the Seattle Times that Gordon’s wealth came from, “hard work, thriftiness and smart investing throughout her life.” [Seattle Times]

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