### 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.

# No Square Sums

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

Shakil wants to remove numbers from the set $\{1, 2, 3,..., 16\}$ so that no two remaining numbers add to make a perfect square. What is the smallest number of numbers that he needs to remove?

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.
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