Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Mr Ross always tells the truth on Thursdays and Fridays but always tells lies on Tuesdays. On the other days of the week he tells the truth or tells lies, at random. For seven consecutive days he was asked what his name was, and on the first six days he gave the following answers, in order: John, Bob, John, Bob, Pit, Bob. What was his answer on the seventh day?
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.