Penta (for January 2002)
Marvellous matrix


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.

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Hint:  The matrix is generated from a matrix which looks like this:

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Answer: