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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. Can you explain why and prove it?

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Weekly Problem 2 - 2013

Weekly Problem 2 -2013

Weekly Problem 39 - 2009

Stage: 2 and 3 Short Challenge Level:

Show that $(1+x+y)^2-(1-x-y)^2$ is divisible by $4$ for all values of $x$ and $y$.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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