The integer 5 can be rewritten as the sum of smaller, repeatable integers. How many different ways can 5 be rewritten?

different ways

The possibilities must be listed: 1 + 1 + 1 + 1 + 1, 1 + 1 + 1 + 2, 1 + 1 + 3, 1 + 4, 1 + 2 + 2, and 2 + 3. So, there are 6 different ways that 5 can be rewritten. It is apparent that there really are no simpler or faster ways of solving this problem. The important thing is to carefully list all the possibilities without missing any; this is best done by being as systematic as possible (and could even involve making tables!) .