Brain Teasers

Knight and Coins

Bob and Jane are taking turns, placing knights and coins respectively on a chessboard. If Bob is allowed to place a knight only on an empty square which is not attacked by another knight, how many pieces at most can he place before running out of moves? Assume that Jane starts second and plays optimally, trying to prevent Bob from placing knights on the board.

Coming soon.

Two Missiles

Two missiles which are 2000 miles apart are shot towards each other. The speed of the first missile is 13000 miles per hour and the speed of the second missile is 17000 miles per hour. Find the distance between the two missiles 2 minutes before they collide.

The distance will be 1000 miles. It does not matter what he starting distance between the missiles is. 2 minutes before collision they will be (13000 + 17000)/30 = 1000 miles apart.

Programmers and Coins

coins programmers

One programmer draws on a sheet of paper several circles in a line, representing coins, and puts his thumb on the first circle, covering the rest with his hand. Then he asks another programmer to guess how many different head-tail combinations are possible if someone flips all the (imaginary) coins on the paper. The second programmer, without knowing the number of circles, takes the pen and writes down a number. Then the first programmer lifts his hand and sees that the correct answer is written on the paper. How did the second programmer manage to do this?

The second programmer wrote down "1" in front of the first circle. When the second programmer lifted his hand, he saw the number "10...00", which is exactly the number of possible head-tail combinations in binary system.

King's Route

king's route

A chess king travels over an entire chess board, passing through every square once, and without intersecting his path, gets back to the initial square. Show that the king has made at most 36 diagonal moves.

The king must visit the 28 perimeter squares in order; otherwise he will create a portion of the board which is inaccessible for him. However, he can not travel from one square to a neighboring one using only diagonal moves. Therefore he must make at least 28 horizontal/vertical moves and at most 64 - 28 = 36 diagonal moves.