On an island live 13 purple, 15 yellow and 17 maroon chameleons. When two chameleons of different colors meet, they both change into the third color. Is there a sequence of pairwise meetings after which all chameleons have the same color?

A blind man has four pills: two red and two blue. The pills are identical in tehrms of shape, size, texture, weight, smell and so on. Only the colors are different. So the blind man cannot distinguish between a red pill and a blue pill. Now the blind man must consume exactly 1 red pill and 1 blue pill. If he consumes two red pills or two blue pills, he will immediately die. What strategy will enable the blind man to ensure that he consumes exactly one pill of each color?

You are given three piles with 5, 49 and 51 pebbles respectively. Two operations are allowed: (a) merge two piles together or (b) divide a pile with an even number of pebbles into two equal piles. Is there a sequence of operations that would result in 105 piles with one pebble each?

Rajeev is trapped atop a building 200m high. He has with him a rope 150m long. There is a hook at the top where he stands. Looking down, he notices that midway between him and the ground, at a height of 100m, there is a ledge with another hook. In his pocket lies a Swiss knife. Hmm... how might he be able to come down using the rope, the two hooks and the Swiss knife?

Mary baked a rectangular cake. Merlin secretly carved out a small rectangular piece, ate it and vanished! The remaining cake has to be split evenly between Mary's two kids. How could this be done with only one cut through the cake?

Consider five holes in a line. One of them is occupied by a fox. Each night, the fox moves to a neighboring hole, either to the left or to the right. Each morning, you get to inspect a hole of your choice. What strategy would ensure that the fox is eventually caught?

Imagine a 3x3x3 wooden cube. How many cuts do we need to break it into twenty-seven 1x1x1 cubes? A cut may go through multiple wooden pieces.

Patient 13 is cured. He wants to pass by all other patients before leaving. But he can't see the same patient twice or he will get sick again. Can he leave from the door in Room 4?

Followup: Instead of a door in room 4, if there were a helicopter in some other room, is it possible to exit the hospital by visiting all other patients but no patient twice?

Peter and Cynthia stand at each end of a straight line segment. Peter sends 50 ants towards Cynthia, one after another. Cynthia sends 20 ants towards Peter. All ants travel along the straight line segment. Whenever two ants collide, they simply bounce back and start traveling in the opposite direction. How many ants reach Peter and how many reach Cynthia? How many ant collisions take place?

An ant crawls from one corner of a room to the diametrically opposite corner along the shortest possible path. If the dimensions of the room are 3 x 4 x 5, what distance does the ant cover?