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?

Magic Sums and Products

How to build your own magic squares.

No Matter

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

Partitioning Revisited

Stage: 3 Challenge Level:

We can show that $14^2 = 196$ by considering the area of a $14$ by $14$ square:
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We can show that $(x + 1)^2 = x^2 + 2x + 1$ by considering the area of an $(x + 1)$ by $(x + 1)$ square:
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Show in a similar way that $(x + 2)^2 = x^2 + 4x + 4$.

Then use the same method to evaluate $(x + 3)^2$ and $(x + a)^2$.