### 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?

# Total Totality

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

This network has nine edges which meet at six nodes. The numbers $1$, $2$, $3$, $4$, $5$, $6$ are placed at the nodes, with a different number at each node. Is it possible to do this so that the sum of the $2$ numbers at the ends of an edge is different for each edge?
Either show a way of doing this, or prove that it is impossible.

More Total Totality is a follow-up short problem to this one.

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.