1. Suppose you’re in a hallway lined with 100 closed lockers
2. Begin by opening all 100 lockers.
3. Close every second locker.

Tenesco Shelving

4. Go to every third locker and close it if it is open, or open it if it is closed (call this toggling the locker).
5. Continue toggling every nth locker on pass number n.
6. Stop on your hundredth pass of the hallway when you will toggle only locker number 100.

How many lockers are open?


Missing Dollar

Tom, Dick, and Harry each paid 10 dollars for a room at the hotel. When the manager found out, he told the desk clerk that Tom, Dick, and Harry were friends of his and they should be charged only $25.

The desk clerk gave the bell boy $5 and told him to return it to Tom, Dick and Harry. The bell boy, however, decided to give them only three dollars and keep two for himself.

hotel porter

If Tom, Dick and Harry each received $1 back, then that means they only paid $27 for the room. With the $2 the bell boy has in his pocket, the total is $29.

What happened to the missing dollar?

Water & Wine Glasses

Start with two glasses, one filled with water, the other filled with wine.
wine glasses
A spoonful of wine is taken from the wine-glass and stirred into the water-glass, then a spoonful is taken out of the water-glass and returned to the wine-glass. The operations are repeated.

Is there more water in the wine-glass than there is wine in the water-glass or the other way round?

Black & White Pebbles

Many years ago when a person who owed money could be thrown into jail, a merchant in London had the misfortune to owe a huge sum to a money lender. The money lender, who was old and ugly, fancied the merchant’s beautiful teenage daughter. He proposed a bargain. He said he would cancel the merchant’s debt if he could have the girl instead.
Ofelia from Pan's Labyrinth
Both the merchant and his daughter were horrified at the proposal. So the cunning money lender proposed that they let Providence decide the matter. He told them that he would put a black pebble and a white pebble into an empty moneybag and then the girl would have to pick out one of the pebbles. If she chose the black pebble she would become his wife and her father’s debt would be cancelled. If she chose the white pebble she would stay with her father and the debt would still be cancelled. But if she refused to pick out a pebble her father would be thrown into jail and she would starve.

Reluctantly the merchant agreed. They were standing on a pebble strewn path in the merchant’s garden as they talked and the moneylender stooped down to pick up the two pebbles. As he picked up the pebbles the girl, sharp eyed with fright, noticed that he picked up two black pebbles and put them into the moneybag. He then asked the girl to pick out the pebble that was to decide her fate and that of her father.

Imagine that you are standing on that path in the merchant’s garden. What would you have done if you had been the unfortunate girl?

-from Lateral Thinking by Edward DeBono

Time Bomb

You have two matches, and two fuses (pieces of string) which each burn for 30 seconds, and a bomb which must go off exactly 45 seconds after you light the fuse.
time bomb
How do you determine exactly 45 seconds, using just these two matches and two fuses?

Note: Cutting one fuse in half won’t solve the problem because the fuses are of different thicknesses, and you can’t be sure how long any cut piece will burn.