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].

Each digit of a long division has been replaced by a dot or the letter A (which stands for a unique digit).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. Here is the division:

\begin{matrix} \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 \end{matrix}

However, Feynman was not the author of this particular puzzle since the same skeleton division [2] 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[3], long before Richard Feynman's letter.

[edit] References

  1. ^ "Dont you have time to think", ISBN 0141021136
  2. ^ Eric W. Weisstein, Skeleton Division at MathWorld.
  3. ^ W. F. Cheney, Jr. (1936). "Problems for Solution: E211-E217". American Mathematical Monthly 43 (5): 304–305. doi:10.2307/2301207.  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.

[edit] External links