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10 replies to this topic

### #1 bonanova

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Posted 15 January 2008 - 11:23 AM

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

[codebox] 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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### #2 Writersblock

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Posted 15 January 2008 - 06:22 PM

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

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Posted 15 January 2008 - 07:17 PM

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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### #4 Writersblock

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Posted 15 January 2008 - 09:32 PM

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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### #5 bonanova

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Posted 15 January 2008 - 10:14 PM

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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### #6 unreality

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Posted 15 January 2008 - 10:52 PM

Spoiler for my answer, I think... but too easy?

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### #7 bonanova

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Posted 16 January 2008 - 04:54 AM

Spoiler for my answer, I think... but too easy?

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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### #8 bonanova

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Posted 17 January 2008 - 08:14 AM

Hint - the spoiler shows the new magic square.
How was it constructed?
Spoiler for new magic square

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### #9 Browne85

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Posted 17 January 2008 - 03:03 PM

Hint - the spoiler shows the new magic square.
How was it constructed?

Spoiler for new magic square

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

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Posted 18 January 2008 - 08:26 PM

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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