Commander

The Magic of Magic Squares !

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Commander    39

The 9x9 Magic Squares use numbers 1 to 81 only once and has the following properties :

 

Each row , column and the two diagonals adds up to 369 and the center most number has to be 41 !

 

There are many solutions and I give here a sample :

 

post-108627-0-48756400-1492773117.jpg

 

 

We can see that 9x9 Square has nine 3x3 Squares and each of these can be a Magic square with numbers out of the 1 to 81 set.

 

I give below a solution with 9 such 3x3 Squares :

 

post-108627-0-83808900-1492775140_thumb.jpg

 

 

It is not possible to have each 3x3 square add up to 123 and the entire row column or diagonal adding to 3x123 = 369

 

Puzzle : Find the best solution such that each 3x3 Square will add to as close a sum to 123 with the least deviation [less or more] from 123 !

 

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Commander    39
Each row , column and the two diagonals adds up to 369 and the center most number has to be 41 !

 

 

This Center Number 41 is true for the case of nine 3x3 Magic Squares where 1-81 numbers are placed in such a way as to contain 9 Mini Magic Squares as required in the Puzzle.

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Commander    39

Some more inputs :

 

If you take the Sample Magic Square given above formed by the known Generation of Odd numbered Magic Squares with sequential writing of 1,2,3 etc upto 81 as shown it adds up to Magic Sum of 369 as given below.

 

post-108627-0-18807300-1493191375_thumb.jpg

 

 

However it can be seen that there are no Mini 3x3 Magic Squares formed within this. There are a set of Mini Diagonals adding upto 123 each as can be seen.

 

Another interesting Solution is given below.

 

post-108627-0-57364400-1493191687_thumb.jpg

 

Here again there are no 9 Mini 3x3 Magic Squares within but all Mini Diagonals are adding upto 123.

 

Our Current Puzzle is therefore to find a Solution such that each of the 9 Mini 3x3 Squares will add up to a Magic Sum as close to 123 as Possible and the Center Mini Square adding to the Magic Sum 123.

 

 

As an aside I give here the Famous Ramanujan Magic Square which adds up to a Magic Sum for every row column & diagonal and also many Rectangular 4 numbers adding up to the same Magic Sum of 139. The first Row gives the Birthday of Ramanujan : 22 12 18 87

 

I set out to find a similar solution for my own Birthday which was quite easy and all the Properties of the Ramanujan Square is fulfilled for a Magic Sum of 101. 139 and 101 are both Prime Numbers.

 

Then I noted that any Birthday can be used to find similar Solution & this is known already !

 

However I give mine here :

 

post-108627-0-82474200-1493192590_thumb.jpg

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Commander    39

I am placing this on Twitter & Facebook too !



Be the FIRST in the UNIVERSE to Solve it !


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Commander    39
Posted (edited)

I am giving the Solution to this Magic Square Puzzle in the Spoiler !

 

 

 

 

For every 3x3 Magic Square the Center Number has to be one third of the Magic Sum.

 

That means for a Magic Sum of 123 the Center number has to be 41 and as we have only one 41 to be used we can not have any two 3x3 MS within 9x9 1-81 MS having 123 as the Magic Sum !

 

I give here the Best Solution I could find !

 

post-108627-0-34148200-1499349396_thumb.jpg

 

 

Edited by Commander

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