Nobody Home

pooh and piglet

A puzzle by S. Sefibekov:

Winnie-the-Pooh and Piglet set out to visit one another. They leave their houses at the same time and walk along the same road. But Piglet is absorbed in counting the birds overhead, and Winnie-the-Pooh is composing a new “hum,” so they pass one another without noticing. One minute after the meeting, Winnie-the-Pooh is at Piglet’s house, and 4 minutes after the meeting Piglet is at Winnie-the-Pooh’s. How long has each of them walked?

Click for Answer

Bright and Early
Image: Wikimedia Commons

Meteors are more commonly seen between midnight and dawn than between dusk and midnight. Why?

Click for Answer

Knife Act

knife act - problem

I have just baked a rectangular cake when my wife comes home and barbarically cuts out a piece for herself. The piece she cuts is rectangular, but it’s not in any convenient proportion to the rest of the cake, and its sides aren’t even parallel to the cake’s sides. I want to divide the remaining cake into two equal-sized halves with a single straight cut. How can I do it?

Click for Answer

Close Dosage

You’re on a drug regimen that requires you to take one pill a day from each of two bottles, A and B. One day you tap one pill into your palm from the A bottle and, inadvertently, two pills from the B bottle. Unfortunately the A and B pills are indistinguishable, and taking more than one B pill per day is fatal. And the pills are very expensive, so you can’t afford to throw out the handful and start over. How can you arrange to take the correct dose without wasting any pills?

Click for Answer

Hour of Babel

A problem from the second Balkan Mathematical Olympiad, 1985:

Of the 1985 people attending an international meeting, no one speaks more than five languages, and in any subset of three attendees, at least two speak a common language. Prove that some language is spoken by at least 200 of the attendees.

Click for Answer