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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 Reader

Age 11 to 14 Challenge Level:

Do this as you read...

Think of a number.
Multiply it by $3$.
Add $6$.
Take away your start number.
Divide by $2$.
Take away your number.

You have finished with $3$!

How does this work?