A little Googling finds that Irene and Craige Schensted wrote a booklet called "The Two Dimensional Abacus". It was apparently published in 1974, and is fairly rare. On Sun, Jun 10, 2018 at 9:00 PM, James Propp <jamespropp@gmail.com> wrote:

According to Martin Gardner's piece "Napier's Abacus" (chapter 8 in "Knotted Doughnuts and Other Mathematical Entertainments"):

Craige Schensted was inspired by Napier's device to invent a chessboard computer on which many astonishing calculations can be made. The basic idea is to allow the columns to be labeled with the powers of one base and the rows to be labeled with the powers of a different base. Each cell represents the product of its row and column numbers. It would require a long chapter to do justice to the elegant ways Schensted found for using such a board to solve problems that otherwise would be difficult. Does anyone know anything about this?

I wonder whether the only extant account of Schensted's device is in Gardner's files of correspondence. I assume that these files are available to scholars. Perhaps someone should seek to publish those letters that contain contributions to mathematics that would otherwise be lost to posterity?

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