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?

If you can please send it to us.
We might be able to put them up on NRICH but we cannot use them unless:

1. You give an account of how you cracked the problem.

2. Any writing besides the actual matrix is sent electronically rather than scanned in and should be in a form that anyone can understand (that includes adults!).

3. You include your name, age and school.