# Maths Product Problem

Take the letters of the alphabet and assign them a numerical value: a = 1, b = 2, c = 3 etc. through to z = 26.

So the word maths is made from the numbers 13, 1, 20, 8 and 19 and if you multiply them together you get 39,520.

Can you find any other words that also have the product 39,520?

This is a great – if tricky – puzzle: you can just leap straight in and try and find an answer.  Or you can use a bit of maths to help you. (Think factors, think prime numbers, think what happens when you multiply by one? All of which may, or may not, help you.)

And it can be used to introduce that often tricky concept of proof: can you prove that the shortest possible word must contain at least 5 letters?

I’ve got a few answers, but I’m not going to share them with you yet. Have a think about it first – you can always give your answers, or proofs, in the comments section. I’ll provide my solutions in a later post, but for now get your thinking caps on and have a go at solving this problem.

Enjoy!

To help you with this puzzle, below is a table with the alphabet and the number assigned to them:

 A B C D E F G H I J K L M 1 2 3 4 5 6 7 8 9 10 11 12 13 N O P Q R S T U V W X Y Z 14 15 16 17 18 19 20 21 22 23 24 25 26

1. Paul Smith
Posted 15/12/2015 at 8:56 pm | Permalink

I believe that I have a four-letter word. Google reveals that they are, amongst other things, types of crusty roll sandwiches from Philadelphia.

• A Maths Teacher
Posted 15/12/2015 at 10:00 pm | Permalink

Curious to know what the word is. Don’t want to give away too much in the comments and spoil the fun of anyone trying to solve the puzzle, but unless I see your four letter word I shan’t be convinced that you have found one that works. The gauntlet has been thrown down!

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