PROBLEM OF THE WEEK

What number is that, which, added separately to 100 and 164, shall make them perfect squares?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

An item is made from lead blanks in a lathe shop. Each blank suffices for 1 item. Lead shavings accumulated for making 6 items can be melted and made into a blank. How many items can be made from 36 blanks?

A man told his son that he would give him $1000 if he could accomplish the following task. The father gave his son ten envelopes and a thousand dollars, all in one dollar bills. He told his son, "Place the money in the envelopes in such a manner that no matter what number of dollars I ask for, you can give me one or more of the envelopes, containing the exact amount I asked for without having to open any of the envelopes. If you can do this, you will keep the $1000." When the father asked for a sum of money, the son was able to give him envelopes containing the exact amount of money asked for. How did the son distribute the money among the ten envelopes?

Can you write down eight eights so that they add up to one thousand?

One is to three as three is to five and five is to four and four is the magic number.

What is the pattern?

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

Take two numbers, such that the square of the first, plus the square of the second, shall equal 8; while the first, plus the product of the first and second, shall equal 6.  What are the two numbers?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

A horse is tied to a five-meter rope in front of an old saloon. Six meters behind the horse is a bale of hay. Without breaking his rope, the horse is able to eat the hay whenever he chooses.

How is this possible?