By Michael H. Pryor AHA!
MAKE’s favorite puzzles. (When you’re ready to check your answers, visit makezine.com/12/aha.)
An evil king has a cellar filled with
1,000 bottles of wine. An equally
evil queen from a neighboring land
plots to kill him and sends a servant
to poison the wine. The king’s guards
catch the servant after he has
poisoned 1 of the 1,000 bottles. The
guards don’t know which bottle was
poisoned, but they know the poison
is so strong that no matter how much
it was diluted, ingesting any amount
will be fatal. Furthermore, it takes
exactly 1 month before it has an effect
(after which it’s fatal immediately).
The king decides he will use 10
prisoners to test the wine. Being an
extremely clever king, how does he
use his 10 prisoners to determine which
bottle is poisoned, and still be able to
drink the rest of the wine at his anniversary
party in 5 weeks’ time?
Black or White?
A Chinese emperor has to choose a
new adviser amongst 3 sages, all of
them equally wise and trustworthy. He
tells them, “To choose one of you, you’ll
play a simple and fair game. In this sack
there are 3 white balls and 2 black balls.
Each of you will be blindfolded and will
pick 1 ball and place it on your head.
After that, the blindfolds will be removed
and each sage in turn will try to guess
the color of the ball upon his head by
observation of the other picked balls.
However, beware! You may pass your
turn whenever you like, but once you
state a color, if it is wrong you will fail
and be disqualified. This way I’ll learn
which among you is the most intelligent.”
Illustrations by Roy Doty
The sages talk briefly to each other and promptly
refuse. Because of their honesty, they know they
cannot willingly mislead each other by providing
false answers when they are not certain. “Emperor,
it’s of no use because the game is not fair and we
must be honest with you and with each other. The
third sage that guesses in the first round will always
know the answer.” The sages then promptly demonstrated this to the emperor, who was so amazed
by their wits that he appointed all 3 as his advisers.
How did they prove it to the emperor?
Michael Pryor is the co-founder and president of Fog Creek Software. He runs a technical interview site at techinterview.org.