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/* CRYPTO, a crypto-arithmetic puzzle */
/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
/* This problem comes from the newsgroup rec.puzzle. The numbers from 1 to 26 are assigned to the letters of the alphabet. The numbers beside each word are the total of the values assigned to the letters in the word (e.g. for LYRE: L, Y, R, E might be to equal 5, 9, 20 and 13, or any other combination that add up to 47). Find the value of each letter under the equations:
BALLET 45 GLEE 66 POLKA 59 SONG 61 CELLO 43 JAZZ 58 QUARTET 50 SOPRANO 82 CONCERT 74 LYRE 47 SAXOPHONE 134 THEME 72 FLUTE 30 OBOE 53 SCALE 51 VIOLIN 100 FUGUE 50 OPERA 65 SOLO 37 WALTZ 34
Solution: 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 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
Reference: Koalog Constraint Solver <http://www.koalog.com/php/jcs.php>, Simple problems, the crypto-arithmetic puzzle ALPHACIPHER. */
set LETTERS :={ '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'};/* set of letters */
set VALUES := 1..card(LETTERS);/* set of values assigned to the letters */
set WORDS;/* set of words */
param total{word in WORDS};/* total[word] is the total of the values assigned to the letters in the word */
var x{i in LETTERS, j in VALUES}, binary;/* x[i,j] = 1 means that letter i is assigned value j */
s.t. phi{i in LETTERS}: sum{j in VALUES} x[i,j] = 1;
s.t. psi{j in VALUES}: sum{i in LETTERS} x[i,j] = 1;
s.t. eqn{word in WORDS}: sum{k in 1..length(word), j in VALUES} j * x[substr(word,k,1), j] = total[word];
solve;
printf{i in LETTERS} " %s", i;printf "\n";
printf{i in LETTERS} " %2d", sum{j in VALUES} j * x[i,j];printf "\n";
data;
param : WORDS : total := BALLET 45 CELLO 43 CONCERT 74 FLUTE 30 FUGUE 50 GLEE 66 JAZZ 58 LYRE 47 OBOE 53 OPERA 65 POLKA 59 QUARTET 50 SAXOPHONE 134 SCALE 51 SOLO 37 SONG 61 SOPRANO 82 THEME 72 VIOLIN 100 WALTZ 34 ;
end;
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