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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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Pyramids

What are the missing numbers in the pyramids?

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Mindreader

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

Stage: 3 Challenge Level: Challenge Level:1

The following solution was sent to us by Josh (Alameda School)

The easiest way of seeing how it works is to use x as the first number.
Multiply by 3 makes it 3 x
Adding 6 makes it 3 x + 6
Taking away the start number makes it 2 x + 6
Then dividing by 2 makes it x + 3
Taking away the original number then leaves 3.

Well done Josh!

Wat Zhiwen Sergius (Anglo-Chines Primary School, Singapore) writes the solution this way... "Let n be the number (3n+6)-n = (2n+6) (2n+6)/2 = (n+3) (n+3)-3 = n