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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.

Multiply the Addition Square

Age 11 to 14 Challenge Level:

Take an addition table from $1$ to $10$ (or any other that you like better!):

addition square from 1 to 10
Now take a $3\times 3$ square of numbers on it, such as this red one:
addition square with two three by three squares highlighted
Now multiply the two diagonally opposite corner numbers together:
three by three square with top row 5, 6, 7
And then find the difference between the two answers:
$5 \times 9 = 45$
$7 \times 7 = 49$
$49 - 45 = 4$
Now try the numbers in the green square:
three by three square with 8, 9, 10 on top row
What is the answer?
Investigate other $3\times 3$ squares.
What do you notice?
Can you explain it?
Now try with $2\times 2$ squares and $4\times 4$ squares.
Can you predict your answers? What is happening?