Six Glasses

Six identical glasses are placed in a row on the table – first three filled with water, and then three empty ones. Can you move just one glass, so that empty and full glasses alternate?

Take the second full glass, pour all of the water into the second empty glass, and then put it back in its place.

Third Business Day

What is the chance that the third business day of a month is Wednesday?

Assuming there is equal chance that the given month begins with any of the seven days of the week, the answer is 3/7. That’s because Saturday and Sunday are non-working days and therefore if the month starts with any of them, the third business day will be still Wednesday.

Missing Pawns

White to play and mate in 4 moves.

Remark: The position on the diagram is one which occurs in actual play.

Notice that the black queen and the black king have switched positions. However, this can happen only if some pawns have been moved. Therefore we can conclude that the bottom row on the diagram is actually the 8th row of the chessboard. All black and all white pieces have reached their respective opposite sides of the board.

Now White’s first move is Kb8-d7. The only moves black can play are with the knights. If Black plays Kb1-a3, Kb1-c3 or Kg1-h3, white mates in 2 more moves – Kd7-c5 and Kc5-d3. If Black moves Kg1-f3, then after Kd7-c5 Black can delay the mate by playing Kf3-e5. However, after the white queen takes it with Qxe5, Kc5-d3 is unavoidable.

Snail on a Tree

A snail is trying to climb a 10-meter poll. Every day it climbs 4 meters up and then during the night slides 3 meters down. How many days are needed for the snail to get to the top of the poll?

Seven days only. After the sixth day, the snail would have climbed 6 meters. During the seventh day, it will climb 4 more meters and will get to the top.

Burn the Ropes

You have two ropes and a lighter. Each of the ropes burns out in exactly 60 minutes, but not at a uniform rate – it is possible for example that half of a rope burns out in 40 minutes and the other half in just 20. How can you measure exactly 45 minutes using the ropes and the lighter?

First, you light up both ends of the first rope and one of the ends of the second rope. Exactly 30 minutes later the first rope will burn out completely and then you have to light up the other end of the second rope. It will take 15 more minutes for the second rope also to burn out completely, for a total of 30 + 15 = 45 minutes.

Mate No Matter What

If White is to play, can he always mate Black in 2 moves, regardless of the moves played before?

The first thing to notice is that since the last move was made by Black, either the king or the rook was moved and therefore Black cannot castle anymore. Now White plays Qa1 and no matter what is Black’s next move, Qh8 gives check-mate.

Ping Pong Ball

Your last ping pong ball falls down into a narrow pipe embedded in concrete one foot deep. How can you get it out undamaged if all you have is your tennis paddle, your your shoe-laces, keys, wallet and a plastic water bottle, which does not fit into the pipe?

Using the plastic bottle, pour water into the pipe so that the ball will rise up.