### Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### Multiplication Magic

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.

### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

# Ben's Game

##### Age 11 to 16 Challenge Level:

The total number they were playing with must be divisible by $3$.

The number of Ben's counters must initially be divisible by $3$, Jack's by $4$ and Emma's by $5$.

It might help to work out the maximum each could have started with -
e.g. Emma could not have started with $25$ counters. Can you work out why?

How many counters could each of them have started with?

Try some possible numbers.