Feynman Long Division Puzzles

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Physicist Richard Feynman sent the following puzzle for his father attached to a letter to his mother in 1939 [1] .[2]

Each digit of a long division has been replaced by a dot or the letter A (which stands for a unique digit). None of the dots are the same as the A digit. The goal is to reconstruct the original figures. The algorithm commonly used in the US calls for the quotient to be in the first line, the divisor to be before the ) and the dividend after it. The quotient is thus (....A..):(.A.) = (..A.)

Here is the division:

\qquad\qquad\quad\,\!\! .\;\, .\;\, A\;\, .\\
.\, A\, .\overline{)\;\, .\;\, .\;\, .\;\, .\;\, A\;\, .\;\, .}\\
\;\! \underline{.\; .\, A\; A}\\
\quad\;\, .\;\, .\;\, .\;\, A\\
\qquad\underline{.\;\, .\;\, A}\\
\qquad\;\;\, .\;\,\, .\;\,\, .\;\,\, .\\
\qquad\quad\!\underline{.\;\, A\;\, .\;\, .}\\
\qquad\qquad\quad\! .\;\; .\;\; .\;\; .\\
\qquad\qquad\quad\! \underline{.\;\; .\;\; .\;\; .}\\
\qquad\qquad\qquad\quad\; 0

However, Feynman was not the author of this particular puzzle since the same skeleton division [3] had been previously proposed as problem E217 in the May 1936 issue of the American Mathematical Monthly by W. F. Cheney, Jr. and its solution by M. J. Turner was later published in the February 1937 issue of the same journal,[4] long before Richard Feynman's letter.


  1. ^ "Don't you have time to think" - UK edition, ISBN 0-14-102113-6
  2. ^ "Perfectly reasonable deviations from the beaten path" - US edition, ISBN 0-7382-0636-9
  3. ^ Weisstein, Eric W., "Skeleton Division", MathWorld.
  4. ^ W. F. Cheney, Jr. (1936). "Problems for Solution: E211-E217". American Mathematical Monthly (Mathematical Association of America) 43 (5): 304–305. doi:10.2307/2301207. JSTOR 2301207.  Solutions by W. F. Cheney, Jr. and M. J. Turner (among other solvers but there is no mention of R. P. Feynman), Vol. 44, No. 2 (Feb., 1937), pp. 105-106.

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