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Edge Match Puzzle

Rotate four signed edge cards into the single valid 2-by-2 board proven by an exhaustive 6,144-state audit.

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How to use

  1. 1.Select an unplaced card, rotate it until the next cell's outer edges show the correct compass letters and its internal motifs complement existing neighbors.
  2. 2.Place cells 1 through 4 in row-major order. Internal edges need the same arc, wave, leaf, or star motif with opposite plus and minus signs.
  3. 3.Use A at rotation 1, B at 2, C at 3, and D at 0 to assemble the uniquely valid board and earn exactly 1,000 points.

About Edge Match Puzzle

Edge Match Puzzle is an original 2-by-2 printmaker's proof built from four cards named Archive A, B, C, and D. Every card owns four edge codes in north, east, south, and west order. Outer sides must show the matching compass boundary, while internal sides must use the same arc, wave, leaf, or star motif with opposite plus and minus signs. All cards, labels, codes, and rules are local product fixtures.

Each card may be rotated through four quarter-turn positions. A clockwise quarter turn moves the previous west edge to north, north to east, east to south, and south to west. The board is filled in fixed row-major order: upper left, upper right, lower left, then lower right. This fixed order makes every partial placement auditable and avoids hidden automatic rearrangement.

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. In degree terms, those positions are 90, 180, 270, and 0 degrees clockwise from the tray orientation. Partial legal placements keep score at zero. Completing all four boundary and internal constraints freezes the board and awards exactly 1,000 points.

Select an unplaced card from the tray, rotate it clockwise or counterclockwise, and place it into the next numbered cell. Keyboard players focus the tray, use Arrow keys to browse, Enter to select, Q or E to rotate, and P to place. The interface shows the selected card face, current quarter turn, board cells, remaining tray cards, distinct illegal count, feedback, and score.

A placement is rejected when any exposed outer side carries a connector instead of the required compass letter, or when an internal side fails to match an already placed neighbor by motif and opposite sign. The first distinct illegal tile-rotation-cell signature is recoverable. Repeating that identical attempt is a no-op. A second distinct illegal attempt closes the proof board. Unknown cards, already placed cards, invalid cells, occupied cells, out-of-order cells, and actions without a selection are atomic no-ops.

Restart returns all four cards to the tray, clears selection, rotations, score, and errors, and restores cell one as the next target. Completion and deadlock freeze selection, cursor movement, rotation, and placement. The shared game shell supplies Restart, best-score display, keyboard guidance, and the Boss Key. There is no shuffle, timer, upload, network call, model, or hidden solver in the product.

Release verification uses a separate literal oracle that owns its own tile table, rotation implementation, boundary checks, connector matcher, permutations, and rotation loops. It evaluates every 4 factorial tile order multiplied by 4 to the fourth rotation combination: 6,144 complete boards. Exactly one candidate satisfies all constraints, and its literal solution is A1, B2, C3, D0.

Tests replay that solution for exact 1,000, try D0 twice at cell one to prove error deduplication, then D1 to reach the second-distinct-error deadlock. They also cover unknown IDs, occupied and out-of-order cells, selection and rotation boundaries, restart, and terminal freezing. The exhaustive proof does not call a production solver to generate expected results.

This is entertainment rather than a published tile system, technical connector specification, visual aptitude test, education credential, or cognitive assessment. The plus and minus signs describe complementary game edges only. All state and drawing remain local in the browser, with no account, external dataset, tracking-based opponent, or new dependency.

Methodology & sources

Define four original four-edge cards, four compass boundary labels, four signed internal motifs, four rotations, and fixed row-major placement. Require exact boundary labels and same-motif opposite-sign internal pairs. Keep partial score zero and award exactly 1,000 on four legal placements; reject invalid selections and cells atomically; deduplicate tile-rotation-cell mismatch signatures; deadlock on the second distinct mismatch; freeze terminal states. Independently enumerate all 4! x 4^4 = 6,144 boards and require exactly one literal solution A1, B2, C3, D0.

Frequently asked questions

Does the puzzle have a unique solution?
Yes. An independent release oracle exhaustively checks all 6,144 tile-order and rotation combinations and finds only A1, B2, C3, D0.
How do internal edges match?
Adjacent sides need the same motif with opposite signs, such as arc plus meeting arc minus. Outer sides require the exact compass boundary letter.
How are illegal placements counted?
The first distinct tile-rotation-cell mismatch is recoverable, an identical repeat is ignored, and the second distinct mismatch closes the run.

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