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    <p>I coded in SWI-Prolog</p> <pre><code>/* File: pack_squares.lp Author: Carlo,,, Created: Nov 29 2012 Purpose: http://stackoverflow.com/questions/13623775/prolog-constraint-processing-packing-squares */ :- module(pack_squares, [pack_squares/0]). :- [library(clpfd)]. pack_squares :- maplist(square, [5,4,3,2], Squares), flatten(Squares, Coords), not_overlap(Squares), Coords ins 1..10, label(Coords), maplist(writeln, Squares), draw_squares(Squares). draw_squares(Squares) :- forall(between(1, 10, Y), ( forall(between(1, 10, X), sumpts(X, Y, Squares, 0)), nl )). sumpts(_, _, [], S) :- write(S). sumpts(X, Y, [[X1,Y1, X2,Y2]|Qs], A) :- ( ( X &gt;= X1, X =&lt; X2, Y &gt;= Y1, Y =&lt; Y2 ) -&gt; B is A+X2-X1+1 ; B is A ), sumpts(X, Y, Qs, B). square(D, [X1,Y1, X2,Y2]) :- X1 + D - 1 #= X2, Y1 + D - 1 #= Y2. not_overlap([_]). not_overlap([A,B|L]) :- not_overlap(A, [B|L]), !, not_overlap([B|L]). not_overlap(_, []). not_overlap(Q, [R|Rs]) :- not_overlap_c(Q, R), not_overlap_c(R, Q), not_overlap(Q, Rs). not_overlap_c([X1,Y1, X2,Y2], Q) :- not_inside(X1,Y1, Q), not_inside(X1,Y2, Q), not_inside(X2,Y1, Q), not_inside(X2,Y2, Q). not_inside(X,Y, [X1,Y1, X2,Y2]) :- X #&lt; X1 #\/ X #&gt; X2 #\/ Y #&lt; Y1 #\/ Y #&gt; Y2. </code></pre> <p>here is the last lines displayed when running <code>?- aggregate_all(count,pack_squares,C).</code>, notably C counts total placements</p> <pre><code>... 0002255555 0002255555 [6,6,10,10] [7,2,10,5] [4,3,6,5] [5,1,6,2] 0000220000 0000224444 0003334444 0003334444 0003334444 0000055555 0000055555 0000055555 0000055555 0000055555 C = 169480. </code></pre>
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    1. POProlog Constraint Processing : Packing Squares
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    1. CO`:- use_module(library(clpfd)).` in place of `:- [...].`
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    2. COThank you, but I'd rather try my own implementation.
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