Free Shikaku Puzzles Online - Rectangle Logic Game

Discover Shikaku, the captivating Japanese rectangle puzzle also known as "Divide by Box", this math logic game challenges you to divide a grid into rectangles and squares according to area constraints. Each number indicates the area (number of cells) that its rectangle must contain. Perfect for developing spatial reasoning and teaching area & perimeter concepts!

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What is Shikaku?

Shikaku (四角に切れ, “Shikaku ni Kire” in Japanese, meaning “cut into squares”) is a logic puzzle invented by Yoshinao Anpuku, a mathematics student at Kyoto University, in 1989. First published in the legendary Japanese puzzle magazine Nikoli, this game quickly became one of the most beloved logic puzzles worldwide among spatial reasoning enthusiasts.

The concept is beautifully simple: you must divide a grid into rectangles and squares while respecting the numbers shown. Each number represents the area (number of cells) of the rectangle or square that must contain it.

🎯 Game Objective

Divide the entire grid into rectangles and squares following these rules:

  • Each rectangle/square contains exactly one number
  • The number indicates the rectangle’s area (number of cells)
  • The entire grid must be completely covered with no overlaps
  • All rectangles must have sides parallel to the grid edges

Example: A “6” can be surrounded by a 1×6, 2×3, or 3×2 rectangle

Example: A “12” can be 1×12, 2×6, 3×4, 4×3, 6×2, or 12×1

Alternative Names

Shikaku is known by several names in English:

  • Divide by Box – emphasizes the division aspect
  • Rectangles – straightforward description
  • Square-it – less common variant name
  • Sikaku – alternative romanization

All these names refer to the same addictive puzzle that has captivated millions of players!

How to Play Shikaku – Complete Rules

Game Rules

Playing Shikaku is easy to learn but challenging to master:

  1. Observe the grid – It contains numbers scattered in certain cells
  2. Draw rectangles – Click and drag to create a rectangle or square
  3. Match the areas – Each rectangle must contain one number equal to its cell count
  4. Cover the entire grid – No cell can remain empty
  5. No overlapping – Rectangles cannot overlap each other
  6. Verify your solution – The puzzle is solved when all rules are satisfied

Game Controls:

  • Left click and drag to draw a rectangle
  • Right click or Ctrl/Shift to erase lines
  • Start at the center of one cell and release at the opposite corner

📐 Educational Value

Shikaku is an excellent teaching tool for:

  • Multiplication facts – A 12 can be 2×6 or 3×4
  • Area and perimeter – Calculate rectangle dimensions
  • Factors and divisors – Find all factor pairs
  • Tessellation – Complete coverage without gaps

Many math teachers use Shikaku in their classrooms!

Expert Strategies for Solving Shikaku Puzzles

Master these techniques to become a Shikaku expert:

1️⃣ Start with Easy Numbers

The “1s” are obvious:

  • A “1” automatically forms a 1×1 square
  • Draw these tiny squares immediately

Prime numbers (2, 3, 5, 7, 11, 13…):

  • They only have two possible shapes: 1×n or n×1
  • Look at available space to determine orientation
  • Example: a “5” can only be 1×5 or 5×1
  • Example: a “7” can only be 1×7 or 7×1

2️⃣ Analyze Corners and Edges

Numbers in corners or along edges have fewer possibilities:

  • Top-left corner: Rectangle can only extend right and down
  • Along an edge: Reduces possible orientations by 50%
  • These constraints make deduction much easier

3️⃣ Look for Large Numbers

High numbers (12, 15, 20…) are often easier to place:

  • They have few combinations that fit the available space
  • A “12” in a 6×6 grid can only be 3×4, 4×3, 2×6, or 6×2
  • Available space often eliminates several possibilities

4️⃣ Space Elimination Technique

Look at the space around a number to eliminate impossible shapes:

  • If an “8” is surrounded by already-drawn rectangles, only certain shapes remain possible
  • Count adjacent free cells in each direction
  • Eliminate shapes that would extend beyond the grid or overlap another rectangle

5️⃣ Forced Rectangles

Identify rectangles that MUST be placed in a certain way:

  • Draw lines between adjacent numbers immediately (they can’t share a rectangle)
  • Look for isolated areas that can only fit one number’s rectangle
  • Check if placing a rectangle one way would orphan cells with no valid placement

6️⃣ Proof by Contradiction

Sometimes mentally testing a shape reveals an impossibility:

  • If placing a 2×4 rectangle creates an area impossible to fill properly
  • Then that rectangle must be 4×2 or another shape instead
  • This technique is powerful but requires strong spatial visualization

7️⃣ Fill Remaining Gaps Last

Towards the end of the puzzle:

  • Empty spaces become obvious
  • Count remaining cells to find which number corresponds
  • If 6 cells remain grouped together, look for an unused “6”

💡 Expert Tip: When stuck, step back and view the grid from a distance. Sometimes patterns become more obvious with a holistic view!

⚠️ Warning: Beginners are tempted to guess, but the true satisfaction of Shikaku comes from solving through pure logic, without random trial and error.

Benefits of Playing Shikaku

Playing Shikaku regularly offers numerous cognitive and educational benefits:

  • Develops Spatial Awareness: Improves your ability to visualize shapes and spaces
  • Strengthens Math Skills: Practices multiplication, factors, and area concepts
  • Boosts Logical Reasoning: Develops deduction and problem-solving abilities
  • Improves Planning: Teaches anticipating consequences of each choice
  • Enhances Concentration: Requires sustained attention to analyze the entire grid
  • Builds Perseverance: Complex puzzles need patience and determination
  • Perfect Teaching Tool: Ideal for teaching area, perimeter, and tessellation
  • Reduces Stress: Relaxing activity that engages the mind positively

Classroom Applications

Many math educators use Shikaku as a pedagogical tool for:

  • Teaching the concept of area in an engaging way
  • Practicing multiplication tables differently
  • Introducing factorization concepts
  • Developing geometry and spatial reasoning skills

Research shows that geometric puzzles like Shikaku can significantly improve students’ understanding of mathematical concepts, particularly in geometry and number theory.

Other Japanese Logic Puzzles

If you love Shikaku, discover our other logic games:

  • Logic Grid Puzzles: Zebra Puzzles and Einstein’s Riddle for deductive reasoning
  • Takuzu: Binary logic puzzles (also known as Binairo)
  • Kyudoku: Sudoku variant with sum constraints
  • Anagram Plus: Word games to expand vocabulary

Each puzzle develops different cognitive skills while providing hours of intelligent entertainment.