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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 3 - 2013

Weekly Problem 3-2013

Weekly Problem 2 - 2013

Stage: 3 Challenge Level:

Think of a number, double it, then add $3$. Multiply your answer by $4$ and from this take away $5$. Now also take away the number you first thought of.