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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?

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What are the missing numbers in the pyramids?

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A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

Mind Reading

Stage: 3 Challenge Level: Challenge Level:1

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.