### 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.

### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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?

# Takeaway Time

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

Since all the students who liked pizza also liked Chinese, and no student liked all three, we can just think about the remaining $25$ students.

Of these, $14$ liked Chinese and $16$ liked Indian. Since each student liked at least one of these, and there are a total of $30$ 'likes', $5$ students must like both Indian and Chinese.

This leaves $11$ students who liked Indian only.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem