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Lizely

Shikaku

Partition a fixed 4 by 4 grid into rule-valid rectangles with touch, keyboard, Undo, exact scoring, and a mechanically proven unique solution.

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How to use

  1. 1.Choose one corner cell and its opposite corner, inspect the highlighted span, then use Place rectangle; keyboard players press Enter on each corner to place immediately.
  2. 2.Make each rectangle contain exactly one clue, match its cell area to that number, and avoid every accepted rectangle; press U or choose Undo to remove the latest accepted region.
  3. 3.Cover all 16 cells with five valid rectangles for exactly 1,000 points before two invalid submissions deadlock the run.

About Shikaku

Shikaku is a rectangular partition puzzle. A numbered clue sits inside each intended region, and your task is to divide the complete grid into axis-aligned rectangles. Every rectangle must contain exactly one clue, and the number must equal that rectangle's area. A clue of 4 could therefore belong to a one-by-four strip or a two-by-two block, but the other clues and the no-overlap rule determine which local choice can participate in the full partition.

This version uses one compact 4 by 4 board authored specifically for Lizely. Its five clue values are 4, 4, 3, 2, and 3, whose sum is all 16 cells. The board is not described as an official, classic, historical, or published Nikoli puzzle. Nikoli is cited for the Shikaku rule set, while Simon Tatham's maintained Rectangles documentation provides an independent description of the same core constraints. The clue coordinates, final arrangement, score, and two-error run behavior are product fixtures created for this game.

To draw with a mouse or touchscreen, select one corner cell and then the opposite corner of the intended rectangle. The highlighted preview includes every cell between those corners. Choose Place rectangle to validate it. If you want a different span, choose another start after the preview or cancel the selection. Keyboard players move the cursor with the Arrow keys. Press Enter once to anchor the first corner, move to the opposite corner, and press Enter again to place immediately. Escape cancels a partial selection, U removes the latest accepted rectangle, and the shared double-Escape gesture still opens the boss screen.

Validation follows the published rules directly. Coordinates must stay inside the four-by-four board. The selected area must contain exactly one numbered clue. Its width multiplied by its height must equal that clue, and none of its cells may already belong to an accepted rectangle. An invalid submission remains unplaced and counts as one mistake, allowing you to inspect the feedback and continue. A second invalid submission deadlocks the run until Restart. Accepted rectangles remain visible, while Undo removes the most recent accepted rectangle without erasing the recorded mistake count.

Each of the five correct rectangles awards exactly 200 points. Covering all 16 cells with five non-overlapping, rule-valid rectangles finishes the puzzle at exactly 1,000 points. Completion and the two-error deadlock are terminal states: later board input, cursor movement, placement attempts, and Undo cannot change the frozen result. Restart returns to the original clues, zero score, zero mistakes, no selection, and no accepted rectangles. This deterministic scoring makes local and production browser checks reproduce the same path and final value.

The released board is checked more rigorously than comparing play against one stored answer. For each clue, the logic enumerates every in-bounds rectangle whose area equals the clue and which contains no other clue. The five clues produce candidate counts of 2, 1, 3, 2, and 1. An exact-cover backtracker chooses one candidate for every clue, rejects overlapping cells, and accepts only a set that covers all 16 board cells. The release test asks for up to two covers and receives exactly one, proving that the authored fixture has a unique solution under the stated rules.

The disclosed golden partition uses rectangles spanning rows 1–2 and columns 1–2; rows 1–2 and columns 3–4; row 3 and columns 1–3; rows 3–4 and column 4; and row 4 and columns 1–3. Automated checks independently confirm each rectangle's clue count and area, the absence of overlap, complete board coverage, exact 1,000-point scoring, out-of-range rejection, area-mismatch rejection, Undo behavior, two-error deadlock, and frozen completion and deadlock states.

Everything runs inside the browser as a small React client game. It sends no grid state to a server, downloads no daily puzzle, requests no account, invokes no random generator, and adds no package dependency. The board uses native buttons with accessible row, column, clue, and rectangle labels. Its four equal columns fit comfortably on a narrow screen, and large selection controls remain available for touch rather than relying on drag precision.

This game is a short recreational logic puzzle, not an intelligence test, cognitive assessment, educational placement measure, health screening, or employment benchmark. The fixed board becomes easier after repetition, and completion time is intentionally not scored. Use the clue arithmetic and exact-cover structure to practice deliberate partitioning: begin with a clue that has few plausible rectangles, consider how each choice affects neighboring clues, use Undo for a legal choice that blocks the remaining space, and aim for the reproducible 1,000-point finish.

Methodology & sources

Enumerate all in-bounds axis-aligned rectangles for each clue and retain only those whose area equals the clue and which contain exactly that one clue. Sort clue candidate sets by size, then run exact-cover backtracking while rejecting occupied cells; accept only covers containing one rectangle per clue and all 16 cells. Runtime placement applies the same coordinate, clue-count, area, and overlap predicates, awards 200 per accepted rectangle, completes at exactly 1,000, deadlocks on the second invalid attempt, and freezes either terminal state.

Frequently asked questions

What makes a rectangle valid in Shikaku?
It must be axis-aligned, stay inside the grid, contain exactly one numbered clue, have an area equal to that clue, and overlap no accepted rectangle.
Does this puzzle have only one solution?
Yes. The release test generates every legal candidate for every clue and uses exact-cover backtracking to prove that this authored 4 by 4 fixture has exactly one complete partition.
Can I play on a phone or without a mouse?
Yes. Tap two corner cells and choose Place rectangle on a phone, or use Arrow keys and Enter for complete keyboard play. Escape cancels a selection and U undoes.
Is this an official Nikoli puzzle or a cognitive test?
No. Nikoli is cited only for the rules. The board is a Lizely-authored recreational fixture and its score is not an intelligence, health, education, or employment measure.

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