#### You may also like ### Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric. ### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules. ### Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

# Magic Matrix

##### Age 7 to 11 Challenge Level:
Here is a "magic" matrix: It doesn't look very magical does it?
This is how you find out the "magic" in the matrix:

Circle any number in the matrix, for example, $5$. Draw a line through all the squares that lie in the same row and column as your selected number: Then circle another number that has not got a line through it, for example, the $1$ in the top right hand corner, and again cross out all squares in the same row and column: Repeat for a third time, for example: Then circle only the remaining number that has no line through it: Try again with a different starting number. What do you notice?

Try the same thing with these two slightly harder matrices:  This problem was made to celebrate NRICH's tenth birthday - perhaps you can see the connection!

Let's try a different one with larger numbers. What is the magic total this time?

I will show you how this kind of matrix works. You can then invent one to try on your friends!

First you need to choose your 'magic total'. As you know, I chose $100$ for the matrix above.
I have chosen: $1, 16, 9, 23, 18, 4, 2$ and $27$. [You can check that together they add to $100$.]

Now make an addition table like this:   