### 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?

# Three Blind Mice

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

After the first mouse has eaten, $\frac{2}{3}$ of the cheese remains. After the second mouse has eaten, $\frac{2}{3}$ of $\frac{2}{3}$, that is $\frac{4}{9}$, of the cheese remains. Finally, after the third mouse has eaten, $\frac{2}{3}$ of $\frac{4}{9}$, that is $\frac{8}{27}$ of the cheese remains. So $\frac{8}{27}$ of the cheese remains.

This problem is taken from the UKMT Mathematical Challenges.
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