Copyright © University of Cambridge. All rights reserved.

## 'Marvellous Matrix' printed from http://nrich.maths.org/

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?