### 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...

# In One... and the Other

##### Stage: 4 Short Challenge Level:

The sequences have common differences of $7$ and $9$ respectively.

The lowest common multiple of $7$ and $9$ is $63$, so the next term after $2005$ to appear in both sequences is $2005 + 63$, that is $2068$.

This problem is taken from the UKMT Mathematical Challenges.
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