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62 lines
1.8 KiB
62 lines
1.8 KiB
/* MONEY, a crypto-arithmetic puzzle */
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/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
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/* This is the classic example of a crypto-arithmetic puzzle published
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in the Strand Magazine by Henry Dudeney:
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S E N D
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+
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M O R E
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---------
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M O N E Y
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In this puzzle the same letters mean the same digits. The question
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is: how to replace all the letters with the respective digits that
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makes the calculation correct?
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The solution to this puzzle is:
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O = 0, M = 1, Y = 2, E = 5, N = 6, D = 7, R = 8, and S = 9.
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References:
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H. E. Dudeney, in Strand Magazine vol. 68 (July 1924), pp. 97, 214.
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(From Wikipedia, the free encyclopedia.) */
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set LETTERS := { 'D', 'E', 'M', 'N', 'O', 'R', 'S', 'Y' };
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/* set of letters */
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set DIGITS := 0..9;
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/* set of digits */
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var x{i in LETTERS, d in DIGITS}, binary;
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/* x[i,d] = 1 means that letter i is digit d */
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s.t. one{i in LETTERS}: sum{d in DIGITS} x[i,d] = 1;
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/* each letter must correspond exactly to one digit */
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s.t. alldiff{d in DIGITS}: sum{i in LETTERS} x[i,d] <= 1;
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/* different letters must correspond to different digits; note that
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some digits may not correspond to any letters at all */
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var dig{i in LETTERS};
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/* dig[i] is a digit corresponding to letter i */
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s.t. map{i in LETTERS}: dig[i] = sum{d in DIGITS} d * x[i,d];
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var carry{1..3}, binary;
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/* carry bits */
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s.t. sum1: dig['D'] + dig['E'] = dig['Y'] + 10 * carry[1];
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s.t. sum2: dig['N'] + dig['R'] + carry[1] = dig['E'] + 10 * carry[2];
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s.t. sum3: dig['E'] + dig['O'] + carry[2] = dig['N'] + 10 * carry[3];
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s.t. sum4: dig['S'] + dig['M'] + carry[3] = dig['O'] + 10 * dig['M'];
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s.t. note: dig['M'] >= 1; /* M must not be 0 */
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solve;
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/* solve the puzzle */
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display dig;
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/* and display its solution */
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end;
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