A problem from Litton Problematical Recreations, which attributes it to Fermat circa 1635:

What is the remainder upon dividing 5999,999 by 7?

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Red White and Blue

I place four balls in a hat: a blue one, a white one, and two red ones. Now I draw two balls, look at them, and announce that at least one of them is red. What is the chance that the other is red?

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Sand Reckoning

Using only a 4-minute hourglass and a 7-minute hourglass, how can you measure 9 minutes?

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Spin Control


We’re playing Russian roulette. The revolver has six chambers, all empty. I put bullets in two adjacent chambers, spin the cylinder, hold the gun to my head, and pull the trigger. It clicks. Now it’s your turn. Before pulling the trigger, you can choose to spin the cylinder again or leave it as it is. Which is better?

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Making Way


A man is 4/7 across a train trestle when he sees a train coming. To get off the trestle, he can run toward the train or away from it. As it happens, in either case he’ll reach safety just as the locomotive passes him. If he runs at 20 kph, how fast is the train going?

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Strictly Speaking

Six logicians finish dinner. The waitress asks, “Do you all want coffee?”

First logician: “I don’t know.”

Second logician: “I don’t know.”

Third logician: “I don’t know.”

Fourth logician: “I don’t know.”

Fifth logician: “I don’t know.”

Sixth logician: “No.”

Who gets coffee and why?

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Good Hands

A surgeon wears sterile gloves both to protect his patient and to protect himself. Can a hard-pressed surgeon with only two pairs of sterile gloves operate on three patients while keeping everyone safe?

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