diff -r d59bea55db9b -r c445c931472f examples/crypto.mod --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/crypto.mod Mon Dec 06 13:09:21 2010 +0100 @@ -0,0 +1,84 @@ +/* CRYPTO, a crypto-arithmetic puzzle */ + +/* Written in GNU MathProg by Andrew Makhorin */ + +/* 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 , + 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;