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