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