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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?

Draught Plans

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

Barbara wants to place draughts on a $4\times 4$ board in such a way that the number of draughts in each row and in each column are all different (she may place more than one draught in a square, and a square may be empty). What is the smallest number of draughts that she would need?
 
 
 
 
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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