%
% Maths challenge 2004-2005 J5
% 
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% My bank card has a 4 digit pin, abcd. I use the following facts to help me
% remember it:
%
% - no two digits are the same
% - the 2-digit number cd is 3 times the 2-digit number ab
% - the 2-digit number da is 2 times the 2-digit number bc
%
% What are the values of a, b, c, and d?
%

var 0..9: a;
var 0..9: b;
var 0..9: c;
var 0..9: d;

% all digits are different (there are at least two more ways of doing this)
constraint a != b /\ a != c /\ a != d /\ b != c /\ b != d /\ c != d;

% the two digit number cd is 3 times the two digit number ab
constraint 10*c + d = 3*(10*a + b);

% The two digit number da is 2 times the two digit number bc
constraint 10*d + a = 2*(10*b + c);

solve satisfy;