An edge matching puzzle places square cards next to each other so that every touching side shares the same motif with opposite signs, and the Edge Match Puzzle variant proves there is exactly one valid 2-by-2 board out of 6,144 audited states. The outer sides of every placed card must show the matching compass boundary letter, while the internal edges must carry the same arc, wave, leaf, or star motif with opposite plus and minus signs. Each card can be rotated through four quarter-turn positions, and the board fills in fixed row-major order from cell 1 to cell 4, so each placement can be audited before the next move is even attempted. A complete legal board freezes the score at exactly 1,000 points, while any partial placement keeps the score at zero. The unique winning board places A at quarter-turn 1, B at quarter-turn 2, C at quarter-turn 3, and D at quarter-turn 0, a result that has been proven by an independent oracle that exhaustively tested all 4 factorial tile orders multiplied by 4 to the fourth power, which is 6,144 complete boards in total.
How the Edge Matching Puzzle Is Built
Every Edge Match Puzzle board is a fixed 2-by-2 grid backed by four hand-defined cards called Archive A, Archive B, Archive C, and Archive D. Each card owns four edge codes in north, east, south, and west order, drawn from a small set of compass boundary letters and four signed internal motifs: arc, wave, leaf, and star. Outer edges point at the compass boundary of the board and must match a specific letter on each side, while inner edges meet another card and must share a motif with opposite signs. There is no shuffle, no timer, and no hidden card drawn from a larger pool, so the only unknowns in any run are which card goes where and which quarter-turn each card is currently facing.
Cards can be rotated in either direction through four discrete quarter-turn positions. A clockwise quarter turn moves the previous west edge to north, the previous north to east, the previous east to south, and the previous south to west. Counterclockwise rotation applies the same quarter-turn cycle in the opposite direction. In degree terms, the four positions are 0, 90, 180, and 270 clockwise from the tray orientation, which lets the audit and the player describe each placement using the same numeric vocabulary.
How to Play Edge Match Puzzle
- Focus the tray and choose an unplaced card. The selected card face and current quarter-turn appear in the inspection area, while the board highlights cell 1 as the next legal target.
- Rotate the card with Q or E until the next cell's outer edges show the correct compass letters and the internal motifs complement any neighbor already in place.
- Place cells 1 through 4 in row-major order: upper left, upper right, lower left, and lower right. Internal edges need the same arc, wave, leaf, or star motif with opposite plus and minus signs.
- Use A at quarter-turn 1, B at quarter-turn 2, C at quarter-turn 3, and D at quarter-turn 0 to assemble the uniquely valid board and earn exactly 1,000 points.
- If a placement fails, note the distinct illegal count, then restart to return every card to the tray, clear the score, and restore cell one as the next target.
Reading Compass Borders and Signed Motifs
Every external edge on a placed card must show the required compass boundary letter for that side of the board. The top row's outer top edges, the bottom row's outer bottom edges, and the left and right columns' outer side edges each have a single correct letter, and a card is rejected if any exposed outer side carries a connector instead of the required letter. This constraint is what gives the puzzle its compass-borders personality and separates the Edge Match Puzzle tool from generic tile-matching games.
Internal edges follow a separate, stricter rule. When two cards sit next to each other, the touching sides must carry the same motif name and opposite signs. Arc plus must meet arc minus, wave plus must meet wave minus, leaf plus must meet leaf minus, and star plus must meet star minus. If both cards show the same motif with the same sign, or if they show different motifs, the placement is rejected and the distinct illegal counter increments. The four signed motifs are the only internal matching vocabulary; there are no wildcards, no rotations of motifs, and no allowance for partial motif overlap.
| Constraint | Applies to | Matching rule |
|---|---|---|
| Compass border | Outer edges of any placed card | Exact compass letter required for that side; connector alone is a rejection. |
| Signed motif | Internal edges between two placed cards | Same motif (arc, wave, leaf, or star) with opposite plus and minus signs. |
| Cell order | Placement sequence | Fixed row-major order: upper left, upper right, lower left, lower right. |
| Rotation | Each card independently | Four quarter-turn positions; clockwise moves west to north. |
The 6,144-State Audit Behind the Unique Solution
What makes this version of the edge matching puzzle verifiable is the exhaustive audit performed during release. The release process multiplies all 4 factorial permutations of the four cards by 4 raised to the fourth power for the rotation positions, which is exactly 6,144 complete board states. A separate literal oracle owns its own tile table, rotation implementation, boundary checks, connector matcher, permutations, and rotation loops, and it does not call the production solver. That independence guarantees the audited number is not just an internal claim but a separate count over the same fixture.
The oracle rejects every board except one. The single survivor is the literal solution A1, B2, C3, D0, meaning Archive A at quarter-turn 1, Archive B at quarter-turn 2, Archive C at quarter-turn 3, and Archive D at quarter-turn 0. The replay suite walks that audited solution to confirm the exact 1,000-point finish, then deliberately breaks the rules to confirm error deduplication: trying D0 twice at cell 1 counts as a single distinct illegal attempt, and trying D1 at cell 1 closes the proof board as the second distinct illegal attempt. The exhaustive proof is built so any reader can reconstruct the same enumeration with the same fixture, which is what separates deterministic edge matching puzzles from apps that rely on procedural generation.
Scoring, Errors, and Restart Behavior
Scoring is intentionally binary. While you build toward the audited solution, the score stays at zero. The instant all four boundary and internal constraints are satisfied in row-major order, the board freezes and the score is set to exactly 1,000. There is no partial credit, no time bonus, and no penalty for how long you took to find the right rotations. The shared game shell still displays the best score across runs, so a single perfect solution is enough to claim the 1,000-point ceiling.
Errors are handled with deduplication. The first distinct tile-rotation-cell mismatch is recoverable: the game remembers that signature and lets you keep playing. Repeating that exact same attempt is treated as a no-op, because nothing meaningful has changed. A second distinct illegal attempt closes the run, freezing the board so you cannot accidentally wander into a third, fourth, or fifth mismatch. Unknown card IDs, already placed cards, invalid cells, occupied cells, out-of-order cells, and actions without a selection are atomic no-ops, meaning the state is unchanged and no error counter moves. Restart always returns all four cards to the tray, clears selection, resets rotations, zeroes the score, erases errors, and restores cell one as the next target, so every fresh attempt is a clean replay of the same 6,144-state audit.
Keyboard Controls for Edge Match Puzzle
The interface shows the selected card face, the current quarter-turn, all four board cells, the remaining tray cards, the distinct illegal count, feedback messages, and the current score, so you always know what the game thinks you are doing. For keyboard play, focus the tray, use Arrow keys to browse, Enter to select, Q or E to rotate, and P to place.
The shared game shell also supplies a Restart button, a best-score display, keyboard guidance, and a Boss Key for quickly hiding the screen. There is no upload step, no network call, no model download, and no hidden solver running inside the browser, and all state and drawing stay local. If you want a different rotation-driven tile challenge with the same keyboard-first ethos, Pipes Puzzle rotates nine fixed pipe tiles until every opening matches a neighbor and all tiles form one connected network without a closed loop, which is a useful companion practice for any edge matching puzzle solver who wants to sharpen rotation logic.