### 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?

# Always a Multiple?

##### Stage: 3 Challenge Level:

First video:

Alison chose 42, added 24 and got the answer 66: "It is! How on earth did you know that?"

Charlie said: "I'm not sure. Let's try to work it out."

Second video:

Alison arranged multilink to show four tens and two units for 42, and two tens and four units for 24.
She then put the four units with the four tens, and the two units with the two tens, giving six lots of eleven.

Charlie imagined a two-digit number $ab$, where $a$ represents the number in the tens column, and $b$ respresents the number in the units. This can be written as $10a+b$. Similarly, $ba$ can be written as $10b+a$.

Charlie added these together to get $11a+11b$, which he wrote as $11(a+b)$.