### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

# Phone Call

##### Stage: 3 and 4 Short Challenge Level:

A new taxi firm needs a memorable phone number. They want a number which has a maximum of two different digits. Their phone number must start with the digit $3$ and be six digits long. How many such numbers are possible?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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