### Consecutive Numbers

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

### 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.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

# The Queen of Hearts

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

The knaves all disagree, so at most one of them can be telling the truth.

If one of them is telling the truth, then four of them are lying, so four ate the tarts. Hence Knave 4 alone is telling the truth.

If all five knaves are lying, then all five ate the tarts. But then this makes knave 5's statement true, which is a contradiction.

Therefore exactly one of the knaves (Knave 4) is telling the truth.

This problem is taken from the UKMT Mathematical Challenges.
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