lemon-project-template-glpk
view deps/glpk/examples/money.mod @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* MONEY, a crypto-arithmetic puzzle */
3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
5 /* This is the classic example of a crypto-arithmetic puzzle published
6 in the Strand Magazine by Henry Dudeney:
8 S E N D
9 +
10 M O R E
11 ---------
12 M O N E Y
14 In this puzzle the same letters mean the same digits. The question
15 is: how to replace all the letters with the respective digits that
16 makes the calculation correct?
18 The solution to this puzzle is:
19 O = 0, M = 1, Y = 2, E = 5, N = 6, D = 7, R = 8, and S = 9.
21 References:
22 H. E. Dudeney, in Strand Magazine vol. 68 (July 1924), pp. 97, 214.
24 (From Wikipedia, the free encyclopedia.) */
26 set LETTERS := { 'D', 'E', 'M', 'N', 'O', 'R', 'S', 'Y' };
27 /* set of letters */
29 set DIGITS := 0..9;
30 /* set of digits */
32 var x{i in LETTERS, d in DIGITS}, binary;
33 /* x[i,d] = 1 means that letter i is digit d */
35 s.t. one{i in LETTERS}: sum{d in DIGITS} x[i,d] = 1;
36 /* each letter must correspond exactly to one digit */
38 s.t. alldiff{d in DIGITS}: sum{i in LETTERS} x[i,d] <= 1;
39 /* different letters must correspond to different digits; note that
40 some digits may not correspond to any letters at all */
42 var dig{i in LETTERS};
43 /* dig[i] is a digit corresponding to letter i */
45 s.t. map{i in LETTERS}: dig[i] = sum{d in DIGITS} d * x[i,d];
47 var carry{1..3}, binary;
48 /* carry bits */
50 s.t. sum1: dig['D'] + dig['E'] = dig['Y'] + 10 * carry[1];
51 s.t. sum2: dig['N'] + dig['R'] + carry[1] = dig['E'] + 10 * carry[2];
52 s.t. sum3: dig['E'] + dig['O'] + carry[2] = dig['N'] + 10 * carry[3];
53 s.t. sum4: dig['S'] + dig['M'] + carry[3] = dig['O'] + 10 * dig['M'];
54 s.t. note: dig['M'] >= 1; /* M must not be 0 */
56 solve;
57 /* solve the puzzle */
59 display dig;
60 /* and display its solution */
62 end;