### Consecutive Numbers

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

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

### 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.

# Weekly Problem 49 - 2011

##### Challenge Level:

Inspector Remorse estimates that he can solve the average murder in $x$ hours, a bank robbery in half that time, and a car theft in one third of the time he takes to solve a bank robbery.

How much time would he expect to take in solving two murders, six car thefts and four bank robberies?

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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