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What’s The Best Way To Drop A Smartphone?

Welcome to FiveThirtyEight’s first weekly installment of The Riddler. On Fridays, I’ll offer up a problem related to the things we hold dear around here — math, logic and probability, of course. These problems, puzzles and riddles will come from lots of top-notch puzzle folks around the world, including you, the readers.

You’ll find one of the puzzles below. Mull it on your commute, dissect it on your lunch break, and argue about it with your friends and lovers. And then, when you’re ready, submit your answer using the form at the bottom! I’ll reveal the solution next week (UPDATE: Dec. 18, 2:30 p.m.: The solution is now available!) and a randomly chosen correct submission will earn a hearty shoutout in this column. Important small print: If you want to be eligible for the shoutout, I need to receive your correct answer before midnight EST tonight. Speed is prized around here, but so is considered thought.

Now, here’s this week’s inaugural Riddler, which comes to us from Laura Feiveson, an economist at the Federal Reserve’s Board of Governors:

You work for a tech firm developing the newest smartphone that supposedly can survive falls from great heights. Your firm wants to advertise the maximum height from which the phone can be dropped without breaking.

You are given two of the smartphones and access to a 100-story tower from which you can drop either phone from whatever story you want. If it doesn’t break when it falls, you can retrieve it and use it for future drops. But if it breaks, you don’t get a replacement phone.

Using the two phones, what is the minimum number of drops you need to ensure that you can determine exactly the highest story from which a dropped phone does not break? (Assume you know that it breaks when dropped from the very top.) What if, instead, the tower were 1,000 stories high?

As is the case with many puzzles, various incarnations of and riffs on this one have become classic, to the point where they’re asked during job interviews at real-life tech firms. The Riddler is proud to help continue this great puzzling tradition.

Need a hint? You can try asking me nicely. Want to submit a puzzle or problem? Email me.

(UPDATE: Dec. 18, 2:30 p.m.): See the solution here!

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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.