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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?

Amazing

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2



A square maze has 9 rooms with gaps in the walls between them. Once a person has travelled through a gap in the wall it then closes behind them. How many different ways can someone travel through the maze from X to Y?





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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