Feynman Long Division Puzzles

Feynman Long Division Puzzles

Physicist Richard Feynman sent the following puzzle for his father attached to a letter to his mother in 1939 [http://www.amazon.com/dp/0141021136/ "Dont you have time to think"] , ISBN 0141021136] .

Each digit of a long division has been replaced by a dot or the letter "A" (which stands for a unique digit).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 in front of the ) and the dividend behind it. The quotient is thus (....A..):(.A.) = (..A.)

Here is the division:

:egin{matrix}qquadqquadquad,!! .;, .;, A;, .\., A, .overline{);, .;, .;, .;, .;, A;, .;, .}\;! underline{.; ., A; A}\quad;, .;, .;, .;, A\qquadunderline{.;, .;, A}\qquad;;, .;,, .;,, .;,, .\qquadquad!underline{.;, A;, .;, .}\qquadqquadquad! .;; .;; .;; .\qquadqquadquad! underline{.;; .;; .;; .}\qquadqquadqquadquad; 0end{matrix}

However, Feynman was not the author of this particular puzzle since the same skeleton division MathWorld | urlname=SkeletonDivision | title=Skeleton Division] 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 cite journal
author = W. F. Cheney, Jr.
title = Problems for Solution: E211-E217
journal = American Mathematical Monthly
volume = 43
issue = 5
year = 1936
pages = 304–305
url = http://links.jstor.org/sici?sici=0002-9890(193605)43%3A5%3C304%3APFSE%3E2.0.CO%3B2-Q
doi = 10.2307/2301207 [http://links.jstor.org/sici?sici=0002-9890(193702)44%3A2%3C105%3AE%3E2.0.CO%3B2-H 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.] , long before Richard Feynman's letter.

References

External links

* [http://problemcorner.org:591/problemcorner.org/FMPro?-db=problems.fp5&-format=revealcomments.html&-lay=all&ProblemName=AMM&ProblemName=E217&-recid=36005&-find= AMM E217 by W. F. Cheney, Jr.]

* [http://dailyfeynmanlongdivisionpuzzles.blogspot.com/ Daily Feynman Long Division Puzzles]

* [http://wiki.keithl.com/?FeynmanPuzzle FeynmanPuzzle - Kwiki]

* [http://thevariableman.blogspot.com/2007/03/screw-suduko-do-feynman-long-division.html Screw Sudoku ... Do Feynman Long Division]


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