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Rock, Paper, Scissors, Double Scissors!

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,1 and you may get a shoutout in next week’s column. If you need a hint, or if you have a favorite puzzle collecting dust in your attic, find me on Twitter.

## Riddler Express

From Patrick Coate, a new and improved version of the game rock-paper-scissors:

Besides the usual three options that players have — rock, paper or scissors — let’s add a fourth option, double scissors, which is played by making a scissors with two fingers on each side (like a Vulcan salute). Double scissors, being larger and tougher, defeat regular scissors, and just like regular scissors, they cut paper and are smashed by rock. The three traditional options interact just as they do in the standard game.

A rock-paper-scissors-double scissors match is always played best two out of three (or, more precisely, first to win two throws, since there can be an unlimited number of ties). There is just one exception: If your opponent throws paper and you throw regular scissors, you immediately win the match regardless of the score.

What is the optimal strategy at each possible score (0-0, 1-0, 0-1, 1-1)? (You can ignore any ties.) What is the probability of winning the match given a 1-0 lead?

## Riddler Classic

Speaking of ways to randomly settle scores, how about some coin flipping? From James Nugent, a numismatic detective problem:

On the table in front of you are two coins. They look and feel identical, but you know one of them has been doctored. The fair coin comes up heads half the time while the doctored coin comes up heads 60 percent of the time. How many flips — you must flip both coins at once, one with each hand — would you need to give yourself a 95 percent chance of correctly identifying the doctored coin?

Extra credit: What if, instead of 60 percent, the doctored coin came up heads some P percent of the time? How does that affect the speed with which you can correctly detect it?

## Solutions to last week’s Riddlers

Congratulations to ÑÑâÐ Andrea Quadroni ÑÑâÐ of Bellinzona, Switzerland, winner of last week’s Express puzzle, and ÑÑâÐ Ashley Piper ÑÑâÐ of Melbourne, Australia, winner of last week’s Classic puzzle! Those puzzles asked you to find the missing values, marked with a “?,” in the two diagrams, known as area mazes, below. For the Express, the missing value was 4 inches:

And for the Classic, the missing value was 32 square inches:

I explain how to calculate both of those answers in the video below:

## Want to submit a riddle?

Email me at oliver.roeder@fivethirtyeight.com.

## Footnotes

1. Important small print: For you to be eligible, I need to receive your correct answer before 11:59 p.m. EDT on Sunday. Have a great weekend!

Oliver Roeder was a senior writer for FiveThirtyEight. He holds a Ph.D. in economics from the University of Texas at Austin, where he studied game theory and political competition.