# Solving postal problem could win million-dollar prize

##### 点击量： 时间：2019-03-14 13:04:01

By Ian Stewart EVER since a Babylonian scribe decided to teach his students arithmetic by setting them problems using the formula “I found a stone but did not weigh it…” mathematicians have celebrated the hidden depths of apparently everyday problems. They have found inspiration in slicing pies, tying knots and spinning coins. But even mathematicians have been surprised by the depth of the mystery that lurks behind an innocent question about postage stamps. Suppose that your post office sells stamps with just two values: 2 cents and 5 cents. By combining these values, you can make up almost any whole number of cents. For example, to post a letter costing 9¢, you could stick one 5¢ stamp and two 2¢ stamps on the envelope. Two values that you cannot achieve are 1¢ and 3¢ – and in fact these are the only impossible amounts. You can produce any even amount using 2¢ stamps – given a big enough envelope – and any odd value from 5¢ upwards, using one 5¢ stamp and multiple 2¢ stamps. This example is typical. Given an unlimited supply of stamps, there is always some key value above which any total can be achieved by sticking the right combination of stamps on the envelope. This is also true if you have more than two denominations of stamp available. But the million-dollar question is this: with n denominations of stamps available, what is that key value? The first person to consider a simple version of this question was James Joseph Sylvester in 1883 (to be precise, he was dealing with coins,