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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 and 7 are adjacent and 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?