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?