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 5 - 2015

Stage: 4 Challenge Level:

The diagram shows four equal discs and a square. Each disc touches its two neighbouring discs. Each corner of the square is positioned at the centre of a disc. The side length of the square is $2/\pi$. What is the length of the perimeter of the figure?

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution