## Instructions

The objective of this challenge is to find sets of four numbers in this magic square that add up to the magic total of 34.

You can click on the numbers to select them. If you make a mistake you can click on a number to deselect it.

Find 14 different ways of making 34 will earn you a level 1 trophy.

Find 21 different ways to earn a level 2 trophy.

Find 28 different ways to earn a level 3 trophy.

Find 35 different ways to earn a level 4 trophy.

Find 42 different ways to earn a level 5 trophy etc.

Sounds easy? Be careful you do not select a group of four numbers you have already found. Duplicates and incorrect totals will send you back to the beginning!

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

Here is the URL which will take you to the Perfect 4 by 4 Magic Square challenge.

Transum.org/Maths/Puzzles/Magic_Square/

Click the image above to go to the Perfect Magic Square challenge which consists of nine partially completed four by four magic squares waiting for your interaction. Puzzle 1 has ten numbers already in place leaving you just six to drag into the correct cells. Puzzle 9 has only two correctly positioned numbers but give it some thought and you should be able to complete it. Good luck.

Richard, Mount Gambier, South Australia

Saturday, July 14, 2018

"When I've found all 86 sets that add up to 34, the puzzle invites me to continue but if I submit another it will either be a repeat of one already found or add up to a different total. So when I've found all 86, shouldn't the puzzle confirm that I've found all of them? (There are 86, aren't there?)."

Transum,

Sunday, July 15, 2018

"Richard, congratulations, you are correct, there are 86 ways altogether. The reason the program didnâ€™t tell you that you had found them all was to test if you knew there were no more. The action to take at that point is to claim your trophy for level 11.

Many other Transum activities ask you to find all the arrangements, combinations or permutations of something and the system confirms when you have finished. I thought this activity should be different and allow students to find their own way of being certain that they have found all possibilities.

Incidentally, only four of the trophies in the last 1000 claimed (at the time of writing) were for level 11.

Thanks so much for taking the time to comment on this activity. "

Friday, May 24, 2019

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.

#### Magic Square

This is the interactive version of the basic three by three magic square with six levels of difficulty.

Transum.org/go/?to=magic

#### Unmagic Square

This interactive activity is like the magic square puzzle but all of the totals should be different.

Transum.org/go/?to=unmagic

#### Prime Square

The sum of the three numbers in each row and each column should be a prime number in this square.

Transum.org/go/?to=psquare

#### Negative Magic

Fill in the missing numbers in four partially completed magic squares containing negative numbers.

Transum.org/go/?to=negativemagic

## Extension

Can you create a magic square containing all the prime numbers between 30 and 102?

For Students:

For All: