Decrease and Conquer Strip Puzzles

Unique Strip Lab is a free interactive browser puzzle about partitioning a two-color grid. Draw cuts only along the internal cell edges. Every resulting connected region must be a straight 1 × 1, 1 × 2, or 1 × 3 strip. No two finished strips may have the same length and color order after reversal. The live inspector reports region sizes, invalid bends or oversize groups, duplicate strip signatures, and the number of active seams while you work.

Three original levels provide a full start, solve, completion, and replay loop. Pointer users can tap one edge or drag across several neighboring edge controls. Keyboard users can focus each seam and press Enter or Space. Undo restores previous seam states, Reset clears the board, and layered hints progress from a general rule to a current-board diagnosis and finally one verified seam. The layout remains usable at a 390 CSS-pixel viewport without horizontal scrolling.

The exact unique-strip partition rule

A legal strip contains one, two, or three consecutive cells in a single row or column. A region that bends, branches, disconnects, or contains more than three cells is invalid. Every legal strip receives a signature made from its length and ordered color pattern. A one-cell A strip is 1:A. An A–B pair is 2:AB. Turning a physical strip around does not make a genuinely different piece, so 2:BA normalizes to the same signature. The same reversal rule applies to three-cell sequences.

A finished board covers every cell with legal regions and uses each normalized signature no more than once. Orientation itself is not part of the signature: a vertical A–B and horizontal B–A still conflict. This explicit definition is used by both the live duplicate detector and the offline-style exact-cover enumerator shipped with the page.

Why “decrease and conquer puzzles” appears in the title

The discovery query contained the phrase “decrease and conquer puzzles.” The static historical page that revealed the actual grid task used the title “Divide and Conquer Puzzles.” Divide-and-conquer and decrease-and-conquer also name algorithm-design strategies, so the words can be ambiguous. Unique Strip Lab does not claim to teach recursion, asymptotic analysis, or either algorithm family. It explains the spelling difference directly and serves the narrower interactive colored-strip partition task.

That boundary matters for search intent and accuracy. Someone seeking an algorithms tutorial should use an algorithms reference. Someone seeking the grid puzzle can read the complete rule here before play, inspect live state, and finish an original level without navigating to an answer image.

Original levels verified by exact-cover enumeration

Every published color grid was created independently for Unique Strip Lab. Before inclusion, the solver enumerated all in-bounds horizontal and vertical strips of length one through three. It normalized the color signature in both reading directions, then used backtracking to select non-overlapping placements that cover every cell without reusing a signature. Search stops after finding two complete covers. A level is published only when the result count is exactly one.

The unit tests run this enumeration again for all three exported levels. They also confirm that each stored solution covers every cell, contains only legal short strips, and has no repeated normalized signature. This is a technical uniqueness claim under the stated rule, not a claim that the puzzle is the only possible artistic or educational treatment of partitioning.

Live region and duplicate-strip feedback

The board begins as one connected region. Adding a seam removes an adjacency between two cells; removing a seam joins it again. A flood-fill recalculates the connected regions after every change. Each region is then checked for one-row or one-column alignment, contiguity, and a length from one through three. Legal regions receive normalized signatures, and repeated signatures are highlighted separately from invalid shapes.

The first hint describes the first violated rule. The second uses current region and duplicate evidence. The third compares the present seam set with the verified unique solution and identifies only one seam to add or remove. It never imports a historical answer GIF, and the player remains responsible for completing the board.

Clean-room scope, local progress, and support

Unique Strip Lab adopts only the abstract mathematical rule. It does not copy Erich Friedman’s GIFs, grids, solutions, text, title treatment, page design, or source code. Its brand, paper-workshop visual, React interface, region inspector, layered hints, generated level data, solver, writing, and completion flow are original. Project notices identify the runtime libraries and ImageGen production artwork.

Local progress stores only a version, completed level identifiers, and an aggregate hint count. No account, answer history, payment, camera, microphone, or location is involved. Read the Privacy Policy, follow the complete controls, or report a reproducible issue through the public support route. The Terms explain that this is casual logic practice, not a graded assessment.