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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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Nine, Ten and One

Weekly Problem 3 - 2013
Can you find the value of t in these equations?

No Matter

Stage: 3 Short Challenge Level: Challenge Level:1

Think of a whole 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.

No matter what your first number was, your answer will be a multiple of which number?
 
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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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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