### 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?

# Think of Two Numbers

##### Stage: 3 Challenge Level:

Here is an alternative and more unusual version of the "Think of a Number" trick which you may have heard of before.

Think of two whole numbers under $10$.

Take one of them and add $1$.
Multiply by $5$.
Add $1$ again.
Double your answer.
Subtract $1$.

Add your second number.
Add $2$.
Double again.
Subtract $8$.
Halve this number and tell me your answer.

From your answer I can work out both your numbers very quickly. How?

Choose some different pairs of numbers and repeat the process.
Can you figure out how the trick works?