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?
How to build your own magic squares.
Weekly Problem 2 -2013
Show that $(1+x+y)^2-(1-x-y)^2$ is divisible by $4$ for all values of $x$ and $y$.
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.