# 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.

Bob can place at most 16 knights. One way to do this is to keep placing knights only on the 32 white squares. In order to see that Jane can prevent Bob from placing more than 16 knights, split the board in four 4x4 grids. Then, group the squares in each grid in pairs, as shown on the image below. If Bob places a knight on any square, then Jane will place a coin on its paired square. This way Bob can place at most one knight on each of the four red squares, one knight on each of the four green squares, one knight on each of the four brown squares, and one knight on each of the four blue squares. Therefore, he can not place more than 64/4 = 16 knights on the board.

# Lakes but No Water

I have forests but no trees.
I have lakes but no water.
I have roads but no cars.

What Am I?

# Four Consecutive Letters

Find four consecutive letters in the alphabet which can be rearranged to spell a common word.

The letters R, S, T, U can be rearranged to spell "RUST".

# 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.

# 5 Lines With 4 Points

On the image below you can see 11 points in the plane placed in such way that there exist 6 lines passing through 4 points each. Can you place 10 points in the plane, such that there are 5 lines passing through 4 points each?

A simple pentagon works:

# June One Line

Add just one line to create a correct equality.

Add one line to the plus to make it a four:

# Mate in the Fourth

The first four moves played by White are 1. f3, 2. Kf2, 3. Kg3, 4. Kh4. If White gets mated in the fourth move, what could be the moves played by Black?

The game proceeds as follows:

1. f3 e5 (or e6)

2. Kf2 Qf6

3. Kg3 Qxf3+

4. Kh4 Be7#

# 2 Matchsticks, 4 Squares

Move only 2 matchsticks so that you get 4 (identical) squares. There should not be any spare matchsticks left.

The solution is shown below.