### The Coconut Problem

**Ten**people land on a deserted island. There they find lots of

**coconuts**and a

**monkeys.**During their first day they gather

**coconuts**and put them all in a

**community pile.**After working all day they decide to sleep and divide them into

**ten equal piles**the next morning.

**hungry**and

**decides**to take his share early. After dividing up the coconuts he finds he is one coconut

**short**of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly

**divisible by 10.**However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up

**hungry**and

**decides**to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to

**1/9 of the total pile**. After dividing them up into

**nine piles**he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the

**second man**on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the

**10th person**to wake up gets the entire pile for himself. What is the smallest number of possible coconuts in the pile, not counting the monkeys?

**Here is that smallest number!**

**Source**