[Math Lair] Benjamin Franklin's Magic Square

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[Benjamin Franklin]Benjamin Franklin, an 18th-century American printer, politician, diplomat, scientist, inventor, etc., etc., enjoyed creating magic squares in his free time.

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In Franklin's autobiography, he mentions that in his youth he had created an 8×8 semi-magic square with a magic sum of 260, which also had the properties that each half-row sums to 130, and that each "bent row", as Franklin described it, summed to 260. An example "bent row" is illustrated in red in the magic square on the right.

Later on in his life, Franklin created a 16×16 semi-magic square with similar properties; in other words, each row or column sums to the magic sum, 2056, each half-row sums to half of 2056, and each "bent row" sums to 2056. In addition, the numbers in any 4×4 square drawn within the magic square sum to 2056. Here is the square tha Franklin created:
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58392672502312181991861671541351221039071
19821923025162738597091102123134155166187
60372852522292201971881651561331241019269
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554223102472342152021831701511381191068774
203214235246112243547586107118139150171182
534421122452362132041811721491401171088576
205212237244132045527784109116141148173180
514619142432382112061791741471421151108378
207210239242151847507982111114143146175178
494817162412402092081771761451441131128180
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6235303254227222195190163158131126999467
1942232262552313463669598127130159162191
6433321256225224193192161160129128979665

You may also be interested in Euler's Knight's Tour Magic Square.

Sources used (see bibliography page for titles corresponding to numbers): 33.

More information on Franklin's magic squares