### Consecutive Numbers

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

### 14 Divisors

What is the smallest number with exactly 14 divisors?

### Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

# Weekly Problem 30 - 2011

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

The diagram shows three touching circles each of radius $5$cm and a line which touches two of them.

Find the total length of the perimeter of the two shaded shapes.

Leave $\pi$ in your answer.

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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