## Marvellous Matrix

This problem was written for new year $2002$.

Circle any number in the matrix, for example, $608$ as below. Draw a line through all the squares that lie in the same row and column as your selected number.

Circle another number which has not got a line through it, for example, $343$ and again rule out all squares in the same row and column.

Repeat for a third time, then circle the remaining number which has not got a line through it.

Add all the circled numbers together. Note your answer.

Try again with a different starting number. What do you notice?

See if you can work out how this matrix works.

Below is a simpler one which might be easier to investigate.

Can you make a similar matrix which generates a different total?

### Why do this problem?

This problem is tricky to do but can form an interesting challenge to those who need it. It requires much addition & subtraction as well as the making and testing hypotheses.

### Key questions

Have you tried adding the diagonals?

Can you get a clue from the way numbers are selected if you look carefully at the way this is forced to happen?

Does it help to look at the diagram in the hint section?

### Possible extension

Learners could make their own puzzle matrices.

### Possible support

Suggest doing a easier problem such as

Shapes on the playground.