### 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.

### Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

### System Speak

Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6

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

In Miss Quaffley's class, one third of the pupils bring a teddy bear to school. Last term, each boy took $12$ books out of the library, each girl took $17$ books and each teddy bear took $9$ books.

In total $305$ books were taken out. How many girls are there in Miss Quaffley's class?

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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