IN BETWEEN performing his role as a founding father of the United States, inventing the lightning rod and coming up with bifocal spectacles, Benjamin Franklin found time to create a frustrating new type of number puzzle.

Some 240 years before Britain was seized by the craze for Su Doku, Franklin set a teaser for Britain’s mathematicians in the form of a “magic square”. One of his number grids, which has been recovered from the archives of the British Library to celebrate the 300th anniversary of his birth, has been reconstructed as a puzzle in today’s Times for readers to solve.

Franklin’s conundrum was so fiendish that he wrote to his friend John Winthrop, a professor of mathematics at Harvard, to rejoice at having foxed the British Empire’s finest minds. “The magic square . . . has occasioned a good deal of puzzling among the mathematicians here,” he wrote. “But no one has desired me to show him my method of disposing the numbers. It seems they wish rather to investigate it themselves.”

Magic squares — grids of numbers in which the rows, columns and both diagonals add up to the same number — date back to Chinese documents written more than 3,000 years ago. Franklin took the traditional grid and rearranged it so that bent diagonal lines, in the shape of chevrons, also added up to the same number.

In his magic square all rows, columns and bent diagonals add up to 2,056. (Unlike traditional magic squares, the diagonals do not add up to the same number.) For the sake of simplicity we have marked only the bent diagonals that point upwards, but solvers will find that bent diagonals in all directions add up to 2,056.

Su Doku addicts will be familiar with magic squares: every row and column of a Su Doku adds up to 45. Solving Franklin’s magic square will be tougher, however, since it involves arithmetic as well as recognising patterns.

Franklin is believed to have printed his magic square on leaflets and handed them out to friends and fellow academics at the Royal Society. Rupert Baker, library manager at the Royal Society, said that Franklin was a regular at the institution when he lived in London in the 1760s. He did not hand out grids with blanks, but challenged mathematicians to work out how he had constructed them.

Franklin was inspired to experiment with number grids after he was shown a French book of magic squares. He was “not willing to be outdone” by the Frenchman, he wrote in his autobiography, and went home that evening to compile a superior square.

But he was not proud of his grids, lamenting in a letter to a friends that he was “rather ashamed to have it known I spent any part of my time in an employment that cannot possibly be of any use to myself or others”.

The first known magic square is mentioned in the Lo Shu, or “book of the river Lo”, an ancient Chinese document that is also the basis for some of the principles of feng shui. Su Doku was first published in 1979 in an American puzzle book under the name “number place”. In 1984 it was introduced to Japan, where it gained mass appeal. The Times first carried the puzzle in November 2004, leading to a national obsession.

Wayne Gould, who compiles Su Doku puzzles for The Times, said that Franklin’s magic square called for different skills from Su Doku because it required arithmetic. “But the kind of person whose mindset makes them want to do Su Doku would want to do this,” he said.

MANY TALENTS

Apart from creating number grids, Benjamin Franklin is also famous for:

inventing the lightning conductor, bifocal spectacles, the medical catheter, flippers, the Franklin stove (a more efficient way of extracting heat from a fire) and the glass harmonica

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