### 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 Queen of Hearts has lost her tarts! She is sure that those knaves who have not eaten the tarts will tell her the truth and the guilty knave will tell lies. When questioned the five knaves declare:

Knave 1
One of us ate them

Knave 2
Two of us ate them

Knave 3
Three of us ate them

Knave 4
Four of us ate them

Knave 5
Five of us ate them

How many of the knaves were honest?

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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