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alpar@9
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1 /* CRYPTO, a crypto-arithmetic puzzle */
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2
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3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
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4
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5 /* This problem comes from the newsgroup rec.puzzle.
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6 The numbers from 1 to 26 are assigned to the letters of the alphabet.
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7 The numbers beside each word are the total of the values assigned to
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8 the letters in the word (e.g. for LYRE: L, Y, R, E might be to equal
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9 5, 9, 20 and 13, or any other combination that add up to 47).
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10 Find the value of each letter under the equations:
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11
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12 BALLET 45 GLEE 66 POLKA 59 SONG 61
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13 CELLO 43 JAZZ 58 QUARTET 50 SOPRANO 82
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14 CONCERT 74 LYRE 47 SAXOPHONE 134 THEME 72
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15 FLUTE 30 OBOE 53 SCALE 51 VIOLIN 100
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16 FUGUE 50 OPERA 65 SOLO 37 WALTZ 34
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17
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18 Solution:
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19 A, B,C, D, E,F, G, H, I, J, K,L,M, N, O, P,Q, R, S,T,U, V,W, X, Y, Z
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20 5,13,9,16,20,4,24,21,25,17,23,2,8,12,10,19,7,11,15,3,1,26,6,22,14,18
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21
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22 Reference:
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23 Koalog Constraint Solver <http://www.koalog.com/php/jcs.php>,
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24 Simple problems, the crypto-arithmetic puzzle ALPHACIPHER. */
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25
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26 set LETTERS :=
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27 { 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M',
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28 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'
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29 };
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30 /* set of letters */
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31
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32 set VALUES := 1..card(LETTERS);
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33 /* set of values assigned to the letters */
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34
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35 set WORDS;
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36 /* set of words */
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37
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38 param total{word in WORDS};
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39 /* total[word] is the total of the values assigned to the letters in
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40 the word */
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41
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42 var x{i in LETTERS, j in VALUES}, binary;
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43 /* x[i,j] = 1 means that letter i is assigned value j */
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44
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45 s.t. phi{i in LETTERS}: sum{j in VALUES} x[i,j] = 1;
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46
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47 s.t. psi{j in VALUES}: sum{i in LETTERS} x[i,j] = 1;
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48
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49 s.t. eqn{word in WORDS}: sum{k in 1..length(word), j in VALUES}
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50 j * x[substr(word,k,1), j] = total[word];
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51
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52 solve;
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53
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54 printf{i in LETTERS} " %s", i;
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55 printf "\n";
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56
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57 printf{i in LETTERS} " %2d", sum{j in VALUES} j * x[i,j];
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58 printf "\n";
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59
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60 data;
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61
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62 param : WORDS : total :=
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63 BALLET 45
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64 CELLO 43
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65 CONCERT 74
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66 FLUTE 30
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67 FUGUE 50
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68 GLEE 66
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69 JAZZ 58
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70 LYRE 47
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71 OBOE 53
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72 OPERA 65
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73 POLKA 59
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74 QUARTET 50
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75 SAXOPHONE 134
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76 SCALE 51
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77 SOLO 37
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78 SONG 61
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79 SOPRANO 82
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80 THEME 72
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81 VIOLIN 100
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82 WALTZ 34 ;
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83
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84 end;
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