### 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?

# Circle Time

##### Stage: 3 Short Challenge Level:

The triangle that joins up the centres of the circles has sides of length 3 cm, 4 cm, 5 cm so must be a right angled triangle by the converse of Pythagoras' Theorem. Therefore the length of the longer arc of the circle $C_1$ is $\frac{3}{4} \times 2\pi \times 1 = \frac{3}{2} \pi$ cm.

This problem is taken from the UKMT Mathematical Challenges.

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