### 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?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Circle of Lies

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

Pierre said, "Just one of us is telling the truth".
Qadr said, "What Pierre says is not true".
Ratna said, "What Qadr says is not true".
Sven said, "What Ratna says is not true".
Tanya said, "What Sven says is not ture".

How many of them were telling the truth?

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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