Choose any three by three square of dates on a calendar page...
Can you explain how this card trick works?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Al, Bertie, Chris and Di have sums of money totalling £150. Al and Bertie have £55 between them and Al and Chris have £65 between them. What is the difference between the amounts that Al and Di have?
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.