### Counting Factors

Is there an efficient way to work out how many factors a large number has?

### 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?

### Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

# Repetitiously

##### Age 11 to 14 Challenge Level:

How are the following recurring decimals related?

 $0.22222222$ ..... $2.22222222$ ...... $22.22222222$ ...... $222.22222222$ ......

How are these recurring decimals related?

$0.2525252525$ ......
$2.5252525252$ ......
$25.252525252$ ......
$252.52525252525$ ......

Which pairs can be related by a sum and which pairs can be related by a multiplication?

The numbers $2.2222222$ ... and $2.525252525252$ ... can be written as fractions. What are they?