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1, 2, 3 Magic Square

Stage: 2 Challenge Level: Challenge Level:1

1, 2, 3 Magic Square

Arrange three $1$s, three $2$s and three $3$s in this square so that every row, column and diagonal adds to the same total.

three by three grid

You might like to use this interactivity to do this problem.

Full screen version:

This text is usually replaced by the Flash movie.




You may like to try this with other sets of three consecutive numbers (numbers which come one after the other).


This problem has been adapted from "Numbers in Your Head" by John Spooner, published by BEAM Education. It can be purchased for £9.50 plus VAT (and handling and delivery) by calling the BEAM orderline on 01242 267 287.

Why do this problem?

This problem requires only simple adding, but also persistence and logical thinking.

Key questions

What do one, two and three add to?
Which of the numbers, when multiplied by three, will come to the total you want in each of the rows?
What do three twos add to?
How many completely different solutions can you find?

Possible extension

Learners could try this activity with other sets of three consecutive numbers.

Possible support

Suggest using the interactivity or counters marked appropriately on a $3 \times 3$ square.