### 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?

### Pyramids

What are the missing numbers in the pyramids?

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

##### Stage: 3 Challenge Level:

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

Now take a $3\times 3$ square of numbers on it, such as this red one:
Now multiply the two diagonally opposite corner numbers together:
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:
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?