#### Problem

By using positive integers, how many different ways can you make a sum that is equal to six?

For example you could use:

3 + 1 + 1 + 1 = 6
4 + 2 = 6
1 + 2 + 3 = 6

(Consider 4 + 2 to be the same as 2 + 4)

#### Solution

Considering the number of 1's used in the sum.

 6x1's: 1+1+1+1+1+1 5x1's: None 4x1's: 1+1+1+1+2 3x1's: 1+1+1+3 2x1's: 1+1+2+2 and 1+1+4 1x1: 1+2+3 and 1+5 0x1's: 2+2+2, 2+4 and 3+3

Giving 10 solutions.

What if 2+4 is considered to be different to 4+2?

Investigate the number of different sums to make all the integers from 1 to 100.

Problem ID: 29 (Jan 2001)     Difficulty: 1 Star

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