### Calendar Capers

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!

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# Out of Line

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Fill in the empty squares with As, Bs, Cs, Ds and Es so that no horizontal, vertical or diagonal line contains a letter more than once (including diagonals like the one A and E are on). Which letter goes in the square marked *?

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.