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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?

Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Mind Reading

Age 11 to 14 Challenge Level:

Many of you sent in excellent solutions to this problem. You tackled it using algebra, in other words using a letter to represent the number that you started with. Thank you to all pupils from Ardingly College who answered the problem in this way, and to Bronya and Caroline from Tattingstone School. Here is Alistair's solution. Alistair, who goes to Histon Junior School, has explained the algebraic steps very clearly:

If X is the number you think of, you start with X
Then when you add 1, you get X + 1
When you double it, it turns into 2X + 2
When you take away 3, it turns into 2X -1
Adding the number you first thought of makes 3X -1
When you add 7 it turns into 3X + 6
When you divide by 3 it turns into 1X + 2
Then take away the number you first thought of (X) it leaves 2.