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Consecutive Numbers

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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

1, 2, 3 Magic Square

Stage: 2 Challenge Level: Challenge Level:1

This was a great problem! I don't think anybody spotted the fact that there was more than one solution, but we had the four different solutions sent to us individually.

Gaven from Forres Primary, Lucy and Richard who go to Flitcham V.A Primary School, and Ruth from Swanbourne House School all arranged their numbers like this:

1st row L to R 132; 2nd row 321; 3rd row 213

Ruth says:

Whichever way you arrange the numbers, there will be one diagonal line with three numbers the same. So you have to work out which of the numbers, when multiplied by three, will come to the total you want in each of the rows.

This number is always the middle number of three when you choose three consecutive numbers.

Well noticed Ruth!

Katrina from Indian Ridge Middle School and Rachel from Histon and Impington Infant School both found another solution:

1sr row L to R 231; 2nd row 123; 3rd row 312

Rachel told us how she went about tackling the problem:

I added up 1, 2 and 3 to make 6, and tried to make each row add up to this. I started putting a 1 in the top right corner, and tried to put one of each number on each row or column. I nearly gave up when I saw all the 2's on the diagonal, but then I spotted that 2 plus 2 plus 2 also adds to 6.

Kim from Bottisham Village College and Natasha and Nathaniel both from Moorfield Junior School sent in a different solution again:

Top row L to R 213; 2nd row 321; 3rd row 132

And the final solution was sent in by William who also goes to Moorfield Junior School:

Top row L to R 312; 2nd row 123; 3rd row 231