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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.

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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?

Snail's Pace

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

A snail is at one corner of the top face of a cube with side length 1m. The snail can crawl at a speed of 1m per hour.

What proportion of the cube's surface is made up of points which the snail could reach within one hour?

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

This problem is taken from the UKMT Mathematical Challenges.
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