Although the alphametic SEVEN+EIGHT=TWELVE conveys a false message, it has several (how many?) valid solutions.

Find the one with the largest W.

In a total of 6 solutions, the largest W (= 5) is in

69298 + 90431 = 159729,

that is next to the last one:

---------
Solutions
---------

| ?- jm([S,E,V,N,I,G,H,T,W,L],[]).

        SEVEN        36465
  +     EIGHT        69781
  =    TWELVE       106246

E = 6,
G = 7,
H = 8,
I = 9,
L = 2,
N = 5,
S = 3,
T = 1,
V = 4,
W = 0 ? ;

        SEVEN        38487
  +     EIGHT        89561
  =    TWELVE       128048

E = 8,
G = 5,
H = 6,
I = 9,
L = 0,
N = 7,
S = 3,
T = 1,
V = 4,
W = 2 ? ;

        SEVEN        58287
  +     EIGHT        80641
  =    TWELVE       138928

E = 8,
G = 6,
H = 4,
I = 0,
L = 9,
N = 7,
S = 5,
T = 1,
V = 2,
W = 3 ? ;

        SEVEN        63732
  +     EIGHT        39841
  =    TWELVE       103573

E = 3,
G = 8,
H = 4,
I = 9,
L = 5,
N = 2,
S = 6,
T = 1,
V = 7,
W = 0 ? ;

        SEVEN        69298
  +     EIGHT        90431
  =    TWELVE       159729

E = 9,
G = 4,
H = 3,
I = 0,
L = 7,
N = 8,
S = 6,
T = 1,
V = 2,
W = 5 ? ;

        SEVEN        85254
  +     EIGHT        50671
  =    TWELVE       135925

E = 5,
G = 6,
H = 7,
I = 0,
L = 9,
N = 4,
S = 8,
T = 1,
V = 2,
W = 3 


-------
Program
-------

jm([S,E,V,N,I,G,H,T,W,L],Type) :-
	domain([S,E,V,N,I,G,H,T,W,L],0,9),
	S#>0,E#>0,T#>0,
	all_different([S,E,V,N,I,G,H,T,W,L]),
	sum(S,E,V,N,I,G,H,T,W,L),
	labeling(Type,[S,E,V,N,I,G,H,T,W,L]).
	
sum(S,E,V,N,I,G,H,T,W,L) :-
				10000*S + 1000*E + 100*V + 10*E + N
	+			10000*E + 1000*I + 100*G + 10*H + T
	#=	100000*T +	10000*W + 1000*E + 100*L + 10*V + E.

Posted by ollie on 2016-12-02 16:22:04