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Adding in Rows

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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Magic Sums and Products

How to build your own magic squares.

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No Matter

Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?

Cubes Within Cubes Revisited

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem demonstrates how a formula can be derived from the context (rather than "pattern-spotting") in a variety of ways.
It also provides practice in the manipulation of algebraic symbols and generates generalities that can promote discussions on equivalent symbolic forms.

A teacher comments:
This was a good opportunity to practise simple and more difficult sequences and generation of formulae, ranging from linear to cubic. All pupils were able to access the problem up to (and beyond) their own "natural" ability (Year 9 set 2).