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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!

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?


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.

One O Five

Age 11 to 14
Challenge Level

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100 but not to tell you which number they have in mind. Then ask them to tell you the remainders when this number is divided by 3, when it is divided by 5 and when it is divided by 7. Now multiply the first remainder by 70, the second remainder by 21 and the third remainder by 15 and add the three answers together. Now subtract multiples of 105 from this total to give as small a positive whole number as possible. This will be the number your friend first thought of. Test this out a few times and explain why it works.