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Question

Consider this 3x3 magic square, which sums horizontally, vertically and diagonally to 45:

``` 5  22  18
28  15   2
12   8  25[/codebox]
Find a way to convert it to another 3x3 magic square that sums to 21.```

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Do you mean to use a single mathmatical operator on all 9 numbers?

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Do you mean to use a single mathmatical operator on all 9 numbers?

Yup.

which sums horizontally, vertically and diagonally to 45
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Just to clarify, I didn't mean a single operator in solving the puzzle - that I knew.

I refer to the means of conversion - does

Find a way to convert it
mean you must do the same mathmatical "thing" to all 9 numbers and get them to "solve" to 21?
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Just to clarify, I didn't mean a single operator in solving the puzzle - that I knew.

I refer to the means of conversion - does mean you must do the same mathmatical "thing" to all 9 numbers and get them to "solve" to 21?

Without commenting on the nature of what you do,

do the same thing to each of the numbers to get a new srt of numbers.

The new set of numbers, each in its respective place, forms a 21 magic square.

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```5 22 18

28 15 2

12 8 25```
subtract 8 from each number
```-3  14 10

20 7 -6

4  0  17```

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28 15 2

12 8 25
`5 22 18`
subtract 8 from each number

20 7 -6

4 0 17
`-3  14 10`

Well, [1] yes that works and [2] it is too easy.

To be more responsive to Writersblock's question: What I have in mind is not mathematical.

The numbers have a property that surprisingly creates a new magic square.

That the new MS sums to 21 is just a piece of information that lets you verify that the MS you will have found is the one I had in mind.

Have Fun ... !

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Hint - the spoiler shows the new magic square.

How was it constructed?

11 7 3
6 5 10
`4  9  8`

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Hint - the spoiler shows the new magic square.

How was it constructed?

```4  9  8

11 7  3

6  5 10```

It is just the number of letters in the original numbers. 5 has 4 letters etc.

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Oddly enough you can also just start with the lowest # in the original square (the 2)

make it a 3... then for each number in sequential order make it a 4, 5, 6, ...

2->3

5->4

8->5

...

28->11

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do the same thing to each of the numbers to get a new srt of numbers.

Bit of a late entry but there is an even simpler solution.

Do this 'mathematical thing' to each number: multiply by zero and add seven

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