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Equal Products

I come across a lot of puzzles and other maths things online and often save them for later, this evening I came across this little puzzle:

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The numbers 2,3,12,14,15,20 and 21 may be divided into two sets so that the product of the numbers in each set is equal. What is that product?

I had saved this over a year ago, and cannot remember where I got it from, but I can see why. It’s a lovely little question that I intend to use as a starter next week and see how my classes get on.

How I approached it

Before you read on have a go at it yourself. Go on, you know you want to……..

Right, good, now you can see if I went about it the same way!

My first thought was that all the fun could be taken out of this by using a calculator, typing all the numbers in and pressing square root. So when I set it I will be adding the line “and which numbers are in each set”, and this is what I set out to find.

Firstly I set out the numbers in terms of their prime factors:

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Then I tallied up the prime factors:

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From this I knew that the product must be 2x2x2x3x3x5x7 which is 2520.

This, of course, answers the original question but I wanted each set. I looked at the numbers and the first think I noticed was tgat 14 and 21 had to be in separate sets, as they had 7 as a factor. I also needed to split 15 and 20, my intuition suggested that 20 and 21 should be in separate boxes, but it was easy to spot that the 2s and 3s, wouldn’t work out so I placed them together and fit the rest on around them.

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A nice little puzzle, I wonder how my classes will find it.

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  1. Stevie D
    May 22, 2015 at 3:52 pm

    If you’re allowed calculators, it’s even easier … just multiply all the numbers together and take the square root!

    • May 22, 2015 at 3:57 pm

      Yes, but that takes the fun out of it.

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