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## 'Adding in Rows' printed from http://nrich.maths.org/

List any 3 numbers.

It is always possible to find a subset of adjacent numbers that
add up to a **multiple of 3** (that is either one, two
or three numbers that are next to each other). For example:

__5, 7__ , 1 |
5 + 7 = 12 (a multiple of 3) |

4,4, __15__ |
15 is a multiple of 3 |

__5,11,2__ |
5 + 11 + 2 = 18 (a multiple of 3) |

Can you explain why and prove it?

What happens if you write a list of 4 numbers?

Is it always possible to find a subset of adjacent numbers that add
up to a multiple of 4?

Can you explain why and prove it?

What happens if you write a long list of numbers (say n
numbers)?

Is it always possible to find a subset of adjacent numbers that add
up to a multiple of $n$?

Can you explain why and prove it?