SEND + MORE + MONEY

2007-05-27

Finding valid and distinct integers for digits S, E, N, D, M, O, R and Y in the equation SEND + MORE = MONEY is a classical constraint programming problem. Here's the slightly modified version of the sample program at Wikipedia constraint programming entry for SWI-Prolog using clp library:

:- use_module(library('clp/bounds')).

sendmore(Digits) :-
   Digits = [S,E,N,D,M,O,R,Y],
   Digits in 0..9,
   S #\= 0,
   M #\= 0,
   all_different(Digits),
                1000*S + 100*E + 10*N + D
              + 1000*M + 100*O + 10*R + E
   #= 10000*M + 1000*O + 100*N + 10*E + Y,
   label(Digits).

Here's what happens when we load the code and run sendmore:

?- consult('money.pl').
%   library(clp/clp_events) compiled into clp_events 0.00 sec, 2,948 bytes
%  library(clp/bounds) compiled into bounds 0.03 sec, 90,992 bytes
% money2.pl compiled 0.03 sec, 91,812 bytes

Yes
?- sendmore(X).

X = [9, 5, 6, 7, 1, 0, 8, 2] ;

No

So, 9567 + 1085 = 10652. AFAI remember, there was a similar question asked to Google's candidate software engineers, which was WWW + DOT = COM. Well, you now know the answer ;) I'll include both examples for my PySWIP Python package which enables to query SWI-Prolog from Python.