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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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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?

Reflected Back

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

Triangle QRS is isosceles and right-angled.

Beatrix reflects the P-shape in the side QR to get an image.

She reflects the first image in the side QS to get a second image.

Finally, she reflects the second image in the side RS to get a third image.

What does the third image look like?

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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