### 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...

# Weekly Problem 4 - 2015

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

Given any positive integer $n$, Paul adds together the distinct factors of $n$, other than $n$ itself.

Which of the numbers $1$, $3$, $5$, $7$ and $9$ can never be Paul's answer?

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution