### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Digit Sum

What is the sum of all the digits in all the integers from one to one million?

# Back of the Queue

##### Stage: 3 Short Challenge Level:
$3$

The units digit of the product is $3$; therefore the remainder when that number is divided by $5$ is also $3$.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.