### 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...

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

Starting at the square containing the $2$, you are allowed to move from one square to the next either across a common edge, or diagonally through a common corner.

How many different routes are there passing through exactly two squares containing a $0$ and ending in one of the squares containing a $9$?

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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