### Consecutive Numbers

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

### 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.

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?

# Spot the Fake

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

One coin among $N$ identical-looking coins is a fake and is slightly heavier than the others, which all have the same weight. To compare two groups of coins you are allowed to use a set of scales with two pans which balance exactly when the weight in each pan is the same. What is the largest value of $N$ for which the fake coin can be identified using a maximum of two such comparisons?

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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