Not-So-Old Chestnuts

The weakest link in a chain will break if loaded with more than 11 pounds. Ignore the weight of the chain.

1. The chain is hanging on a hook on the ceiling and a ten-pound weight is attached to the end. Will the chain break?
2. The chain is threaded over a pulley and a ten-pound weight is attached to each end. Will the chain break?
3. The chain is threaded over a pulley and both ends of the chain are put together and one twenty-pound weight is hooked through the two ends. Will the chain break?

A horse is pulling a wagon up a hill at an increasing speed. Ignoring all masses except those of the horse and the wagon, which of the following statements is correct?

1. The horse pulls on the wagon harder than the wagon pulls on the horse.
2. The horse pulls on the wagon less than the wagon pulls on the horse.
3. The horse pulls on the wagon just as hard as the wagon pulls on the horse.

Langford's problem is named after the Scottish mathematician, C. Dudley Langford. The problem is as follows: Let's take a three-pair number (six digits): two 3s separated by 3 digits; two 2s separated by 2 digits; two 1s separated by 1 digit, as in this example:
3 1 2 1 3 2
Take a 4-pair number (eight digits):
two 4s separated by 4 digits; two 3s separated by 3 digits; two 2s separated by 2 digits; two 1s separated by 1 digit.
? ? ? ? ? ? ? ?

Can you find the solution for 4, 5, 6, 7 or other number pairs?

A square terrace of a palace is tiled with square tiles in a regular grid-like fashion. One day one of the tiles is broken. They can't find a replacement that matches the other tiles, so they call up the local contractor to send men to remove all the remaining tiles, because they will tile it with other tiles or do something else.

The local contractor gets a telephone call and is asked, "Can you send some men over to remove some tiles from a terrace here?" The contractor wants to do the job as quickly as possible, so he wants to send as many men as possible. However, he wants each person to remove an equal number of tiles. So he asks the palace official, "How many tiles do you have there?" The official replies, "I don't know the number. All I can tell you is that they are laid in a square, but one tile is not missing (because it broke). And along each side, the number is bigger than 3 and is a prime number."

So, if you are the contractor, how many men will you send? (Keep in mind that you want to send as many men as possible, but each must have an equal number of tiles to remove.)

Naeem Sheikh

Time 1998. Two old men, Caleb and Erastus, were sitting on a park bench when a young whippersnapper approached.

"You geezers are really old, aren't you? How old are you, anyway?" he asked. They weren't too happy at being called "geezers", so Caleb decided to give him a puzzle.

"I'm as old as the number of years from the first leap year of this century to the first leap year of next century," said Caleb, "and my brother, Erastus here, is as old as the number of years from the last leap year of the last century to the last leap year of this century."

"Well, you must be twins then," said the fresh young man.

"That just shows how ignorant you are, young fella. Now move along before I wither you with sarcasm," said Erastus.

Which is the elder brother?