Loop

This is the puzzle idea I had: you get many identical copies of a polycube, with road segments drawn on some of the faces. You are instructed to assemble them to fill a square footprint with the visible road segments forming a single loop. As you do, a complex landscape comes together[1].

The tool below lets you explore different pieces on square boards of different sizes. For each piece-board combination, there are some number of solutions. Within a solution, you can select the rim height- this a raised ledge that goes around the outer perimeter and hides side faces[2].

Piece

Unfixable

    Fixable

      Solution

      Scores

      Interesting Findings

      (1) Top ★ Loop

      <score 96> PQA_8x8_790_0. no rects! (Very symmetrical. uses all 12 orientations! looks cool/complex. 12 pcs) — BEST

      (2) Top ★ Loop Asymmetrical

      <score 85> PLR+_6x6_198_0 dead ends on solo piece. — BEST

      fallback: PQA_8x8_730_0 (but: no solo dead ends, but has fault lines, translated patterns, used PQA in (1))

      (3) Cute mini ★ Loop solution

      <score 88> BAV_6x6_2_0 - 6 pieces, no rects, every base used exactly 2x, no solo dead ends, no fault lines

      (4) Top non-loop: several good choices here.

      <score 94> LLR_6x6_315_0 - 10 pcs, 0 rects, 4+6 heights, solo dead end

      1. With roads curving up onto vertical surfaces, as seen in the surreal city geometry of Inception (2010), Doctor Strange (2016), Control Resonant (2026), etc. ↩︎

      2. Imagine the pieces of this puzzle come in a box, with instructions to assemble it inside the box. The rim height is the unit height of the inside of that box. Hiding some faces allows for different solutions; in some cases it reduces the number of possibilities and in others it increases them. ↩︎