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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?

Partial Magic

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

The numbers along the leading diagonal total 58, which is therefore the sum of each row and each column. We can now calculate that the number to the left of 10 must be 20 and below that must be 7. Hence x=21

This problem is taken from the UKMT Mathematical Challenges.
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