math - Cryptarithmetic Multiplication Prolog -

i have grasp of idea of crypt arithmetic , addition cannot figure out how multiplication crypt arithmetic problem. it's two*six=twelve or along lines without middle additional part of multiplication problem given. couldn't find online , found constraints problem nothing leads me answers. not sure ask , thought best place.

i want know how solve multiplication crypt arithmetic problem.

i concluded:

         t  w  o *        s   x _________________ t  w  e  l  v  e   t \= 0 means s \= 0 t 1-6 e (o*x) mod 10 o or x cannot 0 or 1 since e has different , 0 or 1 gives same value  either o or x. 

edit: using generate , test method

solve(t,w,o,s,i,x,e,l,v) :-         x = [t,w,o,s,i,x,e,l,v],         digits = [0,1,2,3,4,5,6,7,8,9],         assign_digits(x, digits),         t > 0,          s > 0,         100*t + 10*w + o * 100*s + 10*i + x =:=         100000*t + 10000*w + 1000*e + 100*l + 10*v + e,         write(x).  select(x, [x|r], r). select(x, [y|xs], [y|ys]):- select(x, xs, ys).  assign_digits([], _list). assign_digits([d|ds], list):-         select(d, list, newlist),         assign_digits(ds, newlist). 

trivially constraint logic programming. example, in eclipse prolog:

:- lib(ic). puzzle(vars) :-     [t,w,o,s,i,x,e,l,v] = vars,     vars :: 0..9,     alldifferent(vars),     t #> 0, s #> 0,     (100*t + 10*w + o) * (100*s + 10*i + x) #=        100000*t + 10000*w + 1000*e + 100*l + 10*v + e,     labeling(vars). 

first solution:

[eclipse]: puzzle([t,w,o,s,i,x,e,l,v]). t = 1 w = 6 o = 5 s = 9 = 7 x = 2 e = 0 l = 3 v = 8 yes (0.01s cpu, solution 1, maybe more) ?  

there 3 different solutions:

[eclipse]: puzzle([t,w,o,s,i,x,e,l,v]), writeln([t,w,o,s,i,x,e,l,v]), fail. [1, 6, 5, 9, 7, 2, 0, 3, 8] [2, 1, 8, 9, 6, 5, 0, 3, 7] [3, 4, 5, 9, 8, 6, 0, 1, 7] no (0.02s cpu) 

update - translation swi prolog:

:- use_module(library(clpfd)). puzzle(vars) :-     [t,w,o,s,i,x,e,l,v] = vars,     vars ins 0..9,     all_different(vars),     t #> 0, s #> 0,     (100*t + 10*w + o) * (100*s + 10*i + x) #=        100000*t + 10000*w + 1000*e + 100*l + 10*v + e,     label(vars).