### 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.

### Ladder and Cube

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 25 - 2015

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

A new taxi firm needs a memorable phone number. They want a number which has a maximum of two different digits. Their phone number must start with the digit $3$ and be six digits long. How many such numbers are possible?

This problem is taken from the UKMT Mathematical Challenges.

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