Benjamin Franklin may be best known as the man who flew a kite in a storm, or as the Founding Father of the United States of America whose face appears on the $100 bill. As with most historical figures, though, Franklin has many more attributes worth exploring. Of course here at the Royal Society his scientific, technological and mathematical interests are the areas we tend to concentrate on, and a recent Publishing blog post on Katherine Ollerenshaw’s work with magic squares inspired me to highlight this small part of our archival collections – Benjamin Franklin’s eighteenth century ‘sudoku’.

 

Benjamin Franklin, painted in 1782 by Joseph Wright (American artist, 1756–93)

 

Within the Canton Papers (MS/597) are extracts of a letter from Franklin regarding his magic squares. If we take his 4×4 construction (pictured below) you can see that the idea was to have the numbers in each row, column and diagonal adding up to 34, without repeating a number. Franklin, of course, went further, creating bigger squares – we also have a 6×6 example and a 16×16.

 

MS_597 4x4

Benjamin Franklin’s 4×4 magic square (Royal Society MS/597/2/20)

 

I’ve recreated Franklin’s 6×6 square below, with a couple of numbers removed in case any readers would like to have a go at solving the puzzle themselves – don’t worry, I’ve not made it difficult! This one might be slightly more complicated as the pattern in the diagonals is a little different. This time instead of the whole diagonal adding up to the target figure, they are to be ‘reckon’d by halves, not crossing but turning at right angles from the Centre…’ I’ve left one of these ‘diagonals’ (the sequence 31-5-33-11-14-17) and one column intact as a starting point.

 

magic square

 

The Canton Papers also feature Franklin’s magic circle. Although our copy is a reproduction of the original letter, it remains a fascinating endeavour by Franklin. Here, he describes his attempt to make the solution clearer ‘by using inks of different colours for the several sets of interwoven circles’, and this does make it a rather colourful item amongst the other manuscripts in Canton’s collection:

 

‘A magic circle of circles’ by Benjamin Franklin, from a letter to John Canton, 29 May 1765 (Royal Society MS/597/2/21x)

 

There are various patterns within the circle, and Franklin’s explanation underneath is much more succinct than any I could attempt. The handwriting is tricky to read on screen, though, so you may wish to come and take a look at the originals of the circle and squares here at the Royal Society Library. We also have books on our shelves on Franklin’s mathematical work, such as Benjamin Franklin’s numbers: an unsung mathematical odyssey by Paul C Pasles. We look forward to seeing you!

 

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