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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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