## 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