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Drag the numbers onto the grid so that they are in the row that matches their colour. The challenge is to make all of the A+B and B+C totals correct.


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This is Zygo level 5. You can try a different level:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 Level 11 Level 12

This number arranging puzzle was devised by Les Page and adapted as a Transum Mathematics interactive numeracy puzzle. The Zygo puzzle is copyright (©2006 Les Page) but available for syndication.

This is an ideal activity for those wishing to develop their numeracy skills and logical thinking. There are 12 different levels and each puzzle is created from random numbers every time the page is loaded so you are very unlikely to get the same puzzle twice.

Sign up for a Transum subscription to see the answers to all of the Transum puzzles.

The Zygo Story

Puzzle creator, Les Page, tells the story of how Zygo came to be:

I suppose I've got to blame Zygo onto something, so it has to be that fantastic numbers puzzle Sudoku.

When Sudoku hit the media in 2004 and the craze began I, like many millions of others who love number puzzles, got caught up with the magical 9 x 9 puzzle and became totallyaddicted to it.

I am an ideas man and it wasn't long before I started to think about devising my own unique numbers puzzle having been completely inspired by Sudoku.

It was the 28th May 2006, my 59th birthday, and all the family were around for tea and birthday cake. My grandson Harry had completely worn me out after a rough and tumble on the lounge floor and I was spending a restive five minutes scribbling some numbers on a piece of graph paper. It was then that I had that Eureka moment. I had put three parallel lines of numbers, from 1 to 9, randomly on the graph paper and then added the numbers in each of the top two columns together and put their totals above. Likewise I added the two bottom numbers in each of the two bottom columns together and put their totals below like this:

Zygo diagram 1

It was then that I realised that the middle row of numbers were common to both sums, up and down, and immediately realised I had hit on something. I had found what I was looking for, a unique, new puzzle and shouted, I've got it!. My family took absolutely no notice of me and Harry carried on playing with his cars and Claire my daughter-in-law continued to feed my other 3 month old grandson, Jamie. I could not blame the family

as they all knew I was in my own little private world, always dreaming up bright ideas, which never ever came to anything. They had given me the nickname of The Mad Professor, and were always pulling my leg about it. Secretly I loved it!

But I knew I was on to something. So I decided to make a second copy of the numbers and totals, which was my puzzle solution and marked them with letters on the side like this:

Zygo diagram 2

I then erased all the numbers from the solution in rows A, B and C except for the first column to form the framework of my puzzle like this:

Zygo diagram 3

Then concentrating on the totals I tried to replace the missing numbers. It took me some time to begin with, but after a while I could see a pattern developing. In the puzzle above I could see that there was a total of 3 at the top and this could only mean that A + B was either 1 + 2 or 2 + 1 in A and B. And as number 1 had already been used in row B the answer had to be 1 + 2 in A ad B like this:

Zygo diagram 4

I then decided to write a spreadsheet macro program on my old favourite Lotus 123. I was self taught and had trained myself to learn all the math functions I needed off by heart. It was quite a challenge, but I managed to succeed and eventually produced a nifty little program which produced puzzles instantly at the touch of two keys and Zygo was born.

When completed I copyrighted it in July 2006. I didn't want the same thing to happen to me as Howard Garns who devised Sudoku in 1979 and died in 1989 before getting the chance to see his creation as a worldwide phenomenon that was never given copyright © status!

At first I gave the puzzle several other names. Because of the Japanese origin of Sudoku I tried to think of a Japanese word for my puzzle too. I looked at a Japanese to English translation program on the internet and came up with KonnyuuKu. The Japanese word Konnyuu means adding numbers and Ku means nine, which I thought appropriate.

But later I decided to formulate puzzles with ranges 1 to 5 and 1 to 7 ( mainly for kids ) and 1 to 10, 1 to 11, 1 to 12 and 1 to 13, so the Ku, 9 part of the name became inappropriate.

So I looked for a new name. I considered NouKou, which when translated means Brain Box, but I eventually came up with Zygo after stumbling across it in the Reader's Digest Oxford Complete Wordfinder.

I was looking for an obscure name. So started looking in the Z's. I was on the last page and feeling rather despondent when there it was………….ZYGO!

Zygo- /zigo, ziggo/ comb. Form joining, pairing.

It's a combination word!




The word Zygo incorporated everything involved with the puzzle I had created. You have to find pairs of combination numbers that when added together give totals that form the basis of the entire puzzle. Amazing. No wonder I shouted, Eureka!, at the top of my voice!

What inspired me to carry on and try to eventually get ZYGO recognised by a website like TRANSUM MATHS was my grandson, Harry.

In 2010 when Harry was 10 he came to tea after school and happened to pick up one of my Zygo puzzles and started to solve it and was totally engrossed for about five minutes.

Finished it, grandad!, he shouted. It's great!

He had got it right too. I was so proud.

Later, before he went home, he told me he had really enjoyed doing Zygo and asked me if some of his school friends could try it too.

It was then that I decided to go and see the Headteacher, Mr Ball at Harry's school and to cut a long story short he arranged a ZYGO CHALLENGE with the 10 and 11 year old pupils during lunch hours.

The results of the questionnaire the children and the teachers completed were amazing. I received scores of 9's and 10's out of 10 and some lovely comments from the pupils saying, I love this puzzle. and I wish I could have this on my DS. A lot of the kids drew smiley faces on their questionnaire forms too, which said everything.

A teacher commented, My mum would love this puzzle!

Mr Ball sent me the following letter:

27th January 2011


Dear Les,

Finally got round to doing the ZYGO challenge, the children were really impressed and thoroughly enjoyed it, as you will see from the evaluations enclosed. I would be very interested in any other ZYGO puzzles or material, as we could probably use them in a range of activities across the school.

Thanks again.

Brian Ball


I now have a large portfolio of number puzzles which I have devised over the last 12 years since the birth of ZYGO. One called U+ has been developed professionally as an Android App and I would like to have my own PuzzLesPage website developed with interactive puzzles on it and have more Apps

developed for the Apple Store and Google Play.

Les Page, Author of ZYGO.

If you like this puzzle you may want to try one of the other Transum Puzzles.

Sarah C,

Monday, February 5, 2024

"THIS IS SO FUN, my teacher assigned this as a fun math puzzle and it was the best! Even after the timer ran out, many of my classmates still wanted to keep playing! :3."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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