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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 31 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1
3.

Call your first number $x$. Doubling and adding five gives $2x+5$. Doubling and adding two gives $2(2x+5)+2=4x+12$. Subtracting $x$ then leaves $3x+12=3(x+4)$ which is always a multiple of 3.


This problem is taken from the UKMT Mathematical Challenges.

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