No 39

Square Permutations

 

What have 169, 196 and 961 in common?

They are different PERMUTATIONS of the digits 1,6 and 9. They are also square numbers: 13², 14² and 31². Are there other examples like this?

Try calculating 36², 54² and 96². Can you find more examples?

Is it possible to find more than three squares with this property?

Calculate: 128², 178², 191², 196² and 209² and be amazed!

Now, if you have recovered, then consider: 1024²=1048576.

There are another six square numbers with the same digits but in a different order.

Can you find the six different permutations of 0,1,4,5,6,7 and 8 that give square numbers?

A final thought... 10128²=102576384. This square contains one each of the digits:

0, 1, 2, 3, 4, 5, 6, 7 and 8

Can you find any of the eighty seven square numbers that contain one each of the digits:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

Happy hunting!!

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

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