3x3 magic squares with 6 squares division histograms rev. 1

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A subset of the goal of finding a 3x3 magic square of squares is to find one that contains seven squares. Only one of these has been found to date (by Andrew Bremner.) In an effort to find another, these posters have been developed to help find patterns in the data so that faster non-exhaustive algorithms can be developed.

This is a collection of 24 posters detailing the structure of 3x3 magic squares containing six square numbers.

The posters were created using a dataset of 249347 3x3 magic squares with 6 squares from the Fituvalu project. The dataset does not any contain magic squares with 3 negative values, as that would make the finding of a seventh square impossible.

The posters are 36 inches wide and 65 inches tall, and are archived here in .svg, and .png formats. The files are named in this fashion: 6 where TYPE is 1-16, and SUBTYPE is 1 or 2.

A word about understanding the 3x3 description box:

The A, B, C letters represent a three square progression, where each number is square, proceeds from smallest to largest, and are an equal distance away from each other. A second progression D, E, F is also present, although sometimes one of the letters is not needed. When there is a D and an F, the E is implied to be the same difference away from F as B is from A. Likewise there can be an E and an F and a D is implied to be before E.

The positions of squares follows a well-known structure.
i. (0,1), (2,2), (1,0)
ii. (2,1), (0,0), (1,2)
iii. (0,2), (1,1), (2,0)

A word about types:

There are 16 ways to position 6 squares in a 3x3 grid, which is the basis for the 16 types. Eight of those types can have an extra way to position the three square progressions (ascending vs descending) among the 6 positions which results in a total of 24 posters.

Revision 1. May 2020.

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