### 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...

# Takeaway Time

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

$35$ teenagers were asked what takeaways they liked to eat.

$24$ answered Chinese
$16$ answered Indian
$10$ answered pizza

None of the teenagers liked all three. All who liked pizza also liked Chinese and $9$ of the Chinese fans didn't like either Indian or pizza.

If all the teenagers liked at least one, how many liked only Indian?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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