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# Shared solution to odd numbered grid totals

## Question

I want to share with you the solution to any odd numbered grid,where by the columns , rows ,and diagonals each has the same total. we have all seen the very simple 3 x 3 grid filled with # 1 thru 9 ;   Much more difficult would be a 5 x 5 grid with numbers 1 thru 25 ;    A  7 x 7 grid would be virtually impossible ,but with the few simple rules below any odd numbered grid can be filled as fast as  you can write and all cols ,rows and diagonals total the same

1a) Always start in the square to right of center square
!)    you are always traveling diagonally down to the right;   when you exit the right side,you move down one row then jump left to farthermost open square

2) moving diagonally down to the right.you will exit the bottom..move one column right and jump
up to the highest open square

3)When you are trying to move down and right and you encounter a numbered square
...you go in the upper left corner and out the upper right corner ending on the same row
you started

3 a)  If the above move puts you out side the main grid  then you jump back to the left as far as poss on that row

3 b)  If you are still inside the big grid,then you  move down to the right as before

3 c)  when you exit on the main diagonal  Move to the left as far as possible in the bottom row

4) The above are all repetitive moves and allow you fill in any odd numbered grid such that all columns ,all rows and the diagonals add up to the same sum

## Recommended Posts

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Looks like a variation of the Siamese method for constructing n-odd magic squares.

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