Place value

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.

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers and so on?

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Replace each letter with a digit to make this addition correct.

Can you substitute numbers for the letters in these sums?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.