Shikaku
Partition the entire grid into non-overlapping rectangular and square rooms such that each room contains exactly one numbered clue matching its area.
HISTORICAL ORIGIN LORE
The Lineage of Shikaku
Created and published by Japanese puzzle publisher Nikoli under the title Shikaku ni Kire (meaning "Cut into Rectangles"). The puzzle leverages fundamental prime factorization and geometric bounding to create harmonious spatial tessellations.
SYSTEM MECHANICS & RULES
Rules & Cognitive Architecture
The board is a square or rectangular grid of cells, with numbers displayed in certain cells.
Divide the entire grid into rectangular and square sections.
Every section must contain exactly one number.
The area (number of cells) of each rectangular section must be exactly equal to the number contained within it.
Rectangles cannot overlap and must cover 100% of the grid with no vacant cells left over.
Trained Mental Models
- ▸Prime and composite area factorization visualization
- ▸Spatial tessellation and corner boundary exclusion
- ▸Elimination of competing aspect-ratio orientations
INCLUDED FREE FOREVER
The Three Base Tiers
Gentle
6×6 and 7×7 grids featuring prime numbers (2, 3, 5, 7) that force immediate 1×N orientations.
Standard
8×8 grids featuring composite area values (6, 8, 12) demanding cross-boundary exclusion checks.
Deep
9×9 grids with competing factorizations and corner bottleneck constraints.
BEYOND+ MASTER EDITIONS
The Master Variants for Shikaku
9×9–12×12 Enthusiast Grids
High-density large-format layouts with 144 cells and large composite areas
Expansive layouts up to 12×12 containing large numbers (16, 20, 24, 30) that can form multiple rectangular factorizations (e.g. 2×12, 3×8, 4×6), demanding rigorous spatial deduction.
- ·High-order factorization combinatorial search
- ·Complete 144-cell boundary tessellation
- ·Single-solution guarantee via exact cover algorithms
Dual-Symmetric Tiling
Symmetrically balanced layouts mirroring rooms across dual geometric axes
Layouts engineered with rotational 180° and mirror symmetry, where rectangular rooms on one side reflect counterpart rooms on the opposite side, combining aesthetic harmony with dual-room deductions.
- ·Bilateral & 180° rotational symmetry enforcement
- ·Paired room deduction constraints
- ·Harmonious geometric visual balance
FREQUENTLY ASKED QUESTIONS
Questions on Shikaku Architecture
Can rectangles in Shikaku be long 1×N strips?
Yes. Any valid rectangle of dimensions A × B whose area equals the clue number is permitted, provided it contains no other numbers.
Can any cell be left unassigned?
No. In a solved Shikaku board, 100% of the cells must belong to exactly one rectangle, leaving zero gaps.
How does tactile room drawing work?
You simply drag diagonally from one corner of your intended room to the opposite corner. The UI snaps to valid rectangular boundaries.
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Play Shikaku on Android
Available directly on Google Play with Gentle, Standard, and Deep tiers included free forever.