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    <p>I post a solution showing a possible Prolog coding, in style <em>generate and test</em>. There is some slot where you'll place appropriate arithmetic, just to complete your assignment.</p> <pre><code>%% placing place_squares(Big, Small, Squares) :- place_not_overlapping(Big, Small, [], Squares). place_not_overlapping(Big, Small, SoFar, Squares) :- available_position(Big, Small, Position), \+ overlapping(Small, Position, SoFar), place_not_overlapping(Big, Small, [Position|SoFar], Squares). place_not_overlapping(_Big, _Small, Squares, Sorted) :- sort(Squares, Sorted). overlapping(Size, R*C, Squares) :- member(X*Y, Squares), ... % write conditions here available_position(Big, Small, Row*Col) :- Range is Big - Small + 1, between(1, Range, Row), between(1, Range, Col). </code></pre> <p>after placing, it's easy to display</p> <pre><code>%% drawing draw_squares(Big, Small, Squares) :- forall(between(1, Big, Row), (forall(between(1, Big, Col), draw_point(Row*Col, Small, Squares)), nl )). draw_point(Point, Small, Squares) :- ( nth1(I, Squares, Square), contained(Point, Square, Small) ) -&gt; write(I) ; write('-'). contained(R*C, A*B, Size) :- ... % place arithmetic here </code></pre> <p>the result with requested dimensions, and drawing</p> <pre><code>?- place_squares(5,2,Q),draw_squares(5,2,Q). 1122- 1122- 3344- 3344- ----- Q = [1*1, 1*3, 3*1, 3*3] ; 1122- 1122- 33-44 33-44 ----- Q = [1*1, 1*3, 3*1, 3*4] ; 1122- 1122- 33--- 3344- --44- Q = [1*1, 1*3, 3*1, 4*3] . ... </code></pre> <p>the place_squares/3 output is sorted, to ease displaying, and could as well be used to get rid of symmetry, and get a count of all solutions:</p> <pre><code>9 ?- setof(Q, place_squares(5,2,Q), L), length(L, N). L = [[], [1*1], [1*1, 1*3], [1*1, 1*3, 3*1], [1*1, 1*3, 3*1, ... * ...], [1*1, 1*3, ... * ...|...], [1*1, ... * ...|...], [... * ...|...], [...|...]|...], N = 314. </code></pre> <p>You can note that this accepts boards with 'spare' space. You could filter out such incomplete solutions, to complete your task.</p>
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