_AHA! Puzzle This By Michael H. Pryor

MAKE’s favorite puzzles. (When you’re ready to check your answers, visit makezine.com/07/aha.)

Jelly Beans

There are three jars in front of you that are all mislabeled. You can’t see inside the jars, but one contains red jelly beans, another holds blue jelly beans, and the third has a mix of both (not necessarily a ⁵⁰⁄ 50 mix; it could be a ¹⁄ 99 mix, a ²⁹⁹⁄ 22 mix, etc.). What is the least number of jelly beans you would have to remove from the jars to figure out how to fix the labels?

Mountain Man
At 6 a.m., a man starts hiking up a mountain.
He walks at a variable pace, resting occasionally,
but never actually reversing his
direction. At 6 p.m., he reaches
the top. He camps out overnight,
and the next morning at 6
a.m., he begins his descent
down the mountain. Again,
he walks down the path
at a variable pace, resting
occasionally but always going
downhill. At 6 p.m., he reaches the
bottom. What is the probability
that during the second day,
the man is at a particular
spot at the exact same
time he was there on the
first day?

River Crossing

Illustrations by Roy Doty

Three cannibals and three anthropologists have to cross a river. The boat they have is big enough for only two people at a time. If at any point there are more cannibals on one side of the river than anthropologists, the cannibals will eat the anthropologists. The cannibals will follow all directions given to them by the anthropologists. So what can the anthropologists do to ensure they do not get eaten? Remember, the boat cannot cross the river by itself, so someone has to be in it to row it across each time. And as soon as the boat arrives on the shore, the number of cannibals must be less than or equal to the number of anthropologists on that side.