%%%
%%% Authors:
%%%   Gert Smolka <smolka@ps.uni-sb.de>
%%%
%%% Copyright:
%%%   Gert Smolka, 1998
%%%
%%% Last change:
%%%   $Date: 1999-01-18 22:56:07 +0100 (Mon, 18 Jan 1999) $ by $Author: schulte $
%%%   $Revision: 10513 $
%%%
%%% This file is part of Mozart, an implementation
%%% of Oz 3
%%%    http://www.mozart-oz.org
%%%
%%% See the file "LICENSE" or
%%%    http://www.mozart-oz.org/LICENSE.html
%%% for information on usage and redistribution
%%% of this file, and for a DISCLAIMER OF ALL
%%% WARRANTIES.
%%%

%%% crypto arithmetic
%%% A/BC + D/EF + G/HI = 1
%%% letters must be pairwise digits between 1 and 9
%%%
%%% Solution: 9/12 + 5/34 + 7/68 = 1
%%% Eliminate symmetry by A/BC >= D/EF >= G/HI
%%% Yields redundant 2 constraints:  3(A/BC) >= 1,  3(G/HI) =< 1

declare
proc {Fraction Root}
   sol(a:A b:B c:C d:D e:E f:F g:G h:H i:I) = !Root
   BC = {FD.decl}
   EF = {FD.decl}
   HI = {FD.decl}
in
   Root ::: 1#9
   {FD.distinct Root}
   BC =: 10*B + C
   EF =: 10*E + F
   HI =: 10*H + I 
   A*EF*HI + D*BC*HI + G*BC*EF =: BC*EF*HI
   %% impose order
   A*EF >=: D*BC    
   D*HI >=: G*EF
   %% redundant constraints
   3*A >=: BC
   3*G =<: HI

   {FD.distribute split Root}
end

{ExploreAll Fraction}




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