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Add To Six

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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