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The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Can you create a Latin Square from multiples of a six digit number?

It would be nice to have a strategy for disentangling any tangled ropes...

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Simple additions can lead to intriguing results...

Five equations and five unknowns. Is there an easy way to find the unknown values?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?