### 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?

# Many Matildas

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

The pattern repeats every seven letters, so the name ends on the $7^\text{th}$, $14^\text{th}$, $21^\text{st}$, ... letters, i.e. on every multiple of $7$.

Since $1000 \div 7 = 142 \text{ r}6$, there are $142$ complete copies of the name, and then the $1000^\text{th}$ letter is the sixth letter of the next name. Therefore the $1000^\text{th}$ letter is $d$.

This problem is taken from the UKMT Mathematical Challenges.
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