Over the years, I have encountered a number of interesting puzzles. The difficulty varies and I will refrain from assigning any as it is usually very subjective. Feel free to drop me an email if you have any questions, or if you want to confirm that you found the right answer.

12 ballsWe have 12 balls. 11 of them have the same weight while 1 is different, but we don't know if it's heavier or lighter. We have a balance weighing scale that can compare the weight of its left and right arm (possible results: left heavier, right heavier, or equal). Using the scale 3 times, determine which is the different ball.

The ants

We have a wooden stick of length 1m. We drop a number of ants on it. Each ant goes either to the left, or to the right (lets assume that the stick is very thin) and when they reach the end of the stick, they fall off. All ants move at a constant speed of 1m/hour. When two ants collide, they turn around and walk away. The ants don't have dimensions (think of them as simple points). The question is: what is the minimum time by which it is certain that the stick will have no ants on it?

1 3 4 6

This is one of my favorites; mainly because it is so simple.. and yet so frustrating! :-) Using the numbers 1 3 4 6, exactly once each, and the basic operations (+,-,*,/), get the number 24. No monkey business allowed (e.g. 1 concatenated with 3 giving 13, or 1^{3}=1). You can only use the 4 basic operations I mentioned. However, you can use each operation more than once if you want (e.g. 2 additions, 1 subtraction).

Coins on a table

Two people play the following game: they take turns placing coins on a circular table. Coins can not overlap with each other and they must be fully on the table. One can not move the other person's coins. The player that can not place a coin on the table loses the game. Find a winning strategy for the player who goes first (that means that by following this strategy, the player will be able to win every time, as long as she has the first move). All coins have the same size and of course they are smaller than the table.

The mutilated chessboard

Consider an 8x8 chessboard that is missing the upper left and bottom right corners. We want to fill this mutilated board with dominoes (2x1 blocks), so that all squares are covered. Is it possible? If yes, how? If no, prove it.