Raphael Reischuk

Riddles

This page contains a number of interesting riddles, split into three categories: easy, medium, and hard.
Thanks to Dominique Unruh, Rustan Leino for providing some of the riddles listed below.

Easy

Two cords

You are given two cords that both burn exactly one hour, not necessarily with constant speed. How should you light the cords in order to determine a time interval of exactly 15 minutes?

Medium

One cord

You are given one cord that burns exactly one hour, not necessarily with constant speed. How should you light the cord in order to determine a time interval of 15 minutes? (Hint: solve the corresponding riddle from part "Easy" first.)

Duck and Fox

[Told by Rustan Leino] A duck is swimming at the center of a circle-shaped lake. A fox is waiting at the shore, not able to swim, willing to eat the duck. It may move around the whole lake with a speed four times faster than the duck can swim. Can the duck always reach the shore without being eaten by the fox?

Nine Bottles

[Told by Arnar Birgisson] You are given 9 bottles of delicious red wine out of which one is poisoned. Given two mice (that will die when taken a sip of poisoned wine), how can you find out which bottle is the poisoned one by only performing two tests? If solved, consider the case in which you have 240 bottles, 5 mice, but still two tests. It goes along the same lines...

Hard

Predict the other's coin

Assume the following 3-player game consisting of several rounds. Players A and B build a team, they have one fair coin each, and may initially talk to each other. Before starting the first round, however, no more communication between them is allowed until the end of the game. (Imagine they are separated in different places without any communication infrastructure.) A round of the game consists of the following steps: (1) the team gives one dollar to player C. (2) Both A and B toss their coins independently. (3) Both A and B try to predict the other's coin by telling the guess to C. (No communication: A does not know the outcome of B's coin toss, and vice versa, nor the guess). (4) If C verifies that both A and B guess the other's coin correctly, then C has to give 3 dollars back to the team. Should C play this game? (If you want to play this game being player C against me being player A and a friend of mine being B, please let me know!!)

52 cards

Assume you are given 5 cards from a deck of 52 cards. Your task is to give 4 of them in an ordered way to your teammate such that he/she can determine which card you kept. Your teammate does not know the remaining 47 cards. Is this possible? If so, how is your strategy?

100 boxes

Assume 100 boxes with unique numbers and a hundred people, each having a different name. Each such name is written on an individual sheet of paper, hidden in one of the boxes. Each box is randomly assigned exactly one sheet of paper. The people are asked to find the box that contains his/her name. To this purpose, each person individually enters the room and is allowed to see the content of not more than 50 boxes. No communication to the other people is allowed during the whole game. Further, the room with boxes must not be changed in any way. How big is the highest probability that all of them find the corresponding box?