### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Counting Factors

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

# Factor Sum

##### Age 11 to 14 ShortChallenge Level

• $1:$ yes, all primes
• $3=1+2$ e.g. $4$
• $5=1+4$ impossible as if $4$ is a factor then $2$ is as well
$5=1+2+2,1+1+3$ no other possible ways.
• $7=1+2+4$ e.g. $8$
• $9:1+2+5=8$, $1+2+7=10$, $1+3+5=9$ and $1,3,5$ are factors of $15$
So only $5$ is impossible.