Fillomino Puzzles: The Complete Guide to Polyomino Number Logic
Master the art of growing, shaping, and separating numbered regions — from your first 1-clue to advanced parity deductions.
<nav class="toc">
<strong>Table of Contents</strong>
<a href="#what-is-fillomino">What Is Fillomino?</a>
<a href="#three-rules">The Three Core Rules</a>
<a href="#polyomino-shapes">Understanding Polyomino Shapes</a>
<a href="#no-touch-rule">The No-Touch Principle</a>
<a href="#eight-techniques">8 Core Solving Techniques</a>
<a href="#worked-example">Worked 5×5 Example</a>
<a href="#advanced-strategies">Advanced Strategies</a>
<a href="#comparison">Fillomino vs Other Logic Puzzles</a>
<a href="#faq">FAQ</a>
</nav>
<h2 id="what-is-fillomino">What Is Fillomino?</h2>
<p>Fillomino (フィ ル オ ミ ノ, pronounced "fill-oh-MEE-noh") is a number-placement logic puzzle first published by <strong>Nikoli</strong>, the Japanese puzzle company that also popularized Sudoku, Kakuro, and dozens of other logic puzzle types. The name comes from "filling" a grid with <strong>polyominoes</strong> — connected groups of cells where every cell in a group carries the same number, and that number tells you exactly how many cells the group contains.</p>
<div class="info-box">
<h4>🧩 Why Fillomino Is Worth Your Time</h4>
<p>Unlike Sudoku (where regions are fixed 3×3 boxes), Fillomino's regions are <em>flexible shapes</em> that you must grow, bend, and separate through spatial reasoning. A group of 5s can be an L-shape, a T-shape, a zigzag, or a straight bar — as long as all five cells are connected and contain the number 5. This spatial creativity makes Fillomino a refreshing change from row-and-column puzzles while training the same logical deduction muscles. If you enjoy <a href="/guides/nonogram-picross-puzzles-guide/">Nonogram puzzles</a> (where you deduce filled/empty patterns from clues), Fillomino adds a layer of shape-building that feels like sculpting with numbers.</p>
</div>
<p>The puzzle grid starts with a few cells pre-filled with numbers (called <strong>givens</strong> or <strong>clues</strong>). Your job is to fill every remaining empty cell with a positive integer so that the three core rules are satisfied everywhere on the board. Every well-formed Fillomino has exactly one solution, reachable through pure logic — no guessing required.</p>
<h2 id="three-rules">The Three Core Rules of Fillomino</h2>
<p>Fillomino's entire puzzle logic rests on just three rules. Learn these cold — every technique in this guide derives from them.</p>
<div class="strategy-grid">
<div class="strategy-card">
<h3>Rule 1: Size Matching</h3>
<p>Every connected group of identical numbers must contain <strong>exactly as many cells as the number itself</strong>. A group of 3s has exactly 3 cells. A group of 7s has exactly 7 cells. A single 1 is a complete one-cell group.</p>
<p>This is the engine of the puzzle: the number tells you both <em>what</em> to write and <em>how big</em> the region must be.</p>
</div>
<div class="strategy-card">
<h3>Rule 2: No-Touch (No-Merge)</h3>
<p>Two <strong>separate</strong> groups with the same number cannot be orthogonally adjacent (sharing an edge). If they were, they would merge into one larger group — and that merged group would violate Rule 1 because it would have too many cells.</p>
<p><strong>Diagonal touching is allowed.</strong> Two groups of 3s can touch at corners without merging.</p>
</div>
<div class="strategy-card">
<h3>Rule 3: Full Coverage</h3>
<p><strong>Every cell</strong> in the grid must be filled with a positive integer. No empty cells remain when the puzzle is solved. Every cell belongs to some group.</p>
<p>If an empty cell is completely surrounded by borders (finished groups on all sides), it must be a 1 — a one-cell group of its own.</p>
</div>
</div>
<div class="tip-box">
<h4>💡 The Numbers Are Not Limited to Givens</h4>
<p>A common beginner misconception: you can only write numbers that already appear as clues. <strong>Wrong.</strong> You can (and must) introduce new numbers that never appeared in the starting grid. If six empty cells are completely surrounded by finished groups, those six cells must all contain 6 — even if the number 6 never appeared as a clue. Recognizing when to introduce new numbers is a hallmark of experienced solving.</p>
</div>
<h2 id="polyomino-shapes">Understanding Polyomino Shapes</h2>
<p>A <strong>polyomino</strong> is a shape made by connecting squares edge-to-edge. The prefix tells you how many squares: a 1-omino (monomino) is one cell, a 2-omino (domino) is two cells, a 3-omino (tromino) is three cells, and so on. In Fillomino, each number defines a polyomino of that size — a group of 4s is a tetromino (one of the 5 classic four-cell shapes), a group of 5s is a pentomino, and so forth.</p>
<div class="fill-board">
<svg viewBox="0 0 500 120" xmlns="http://www.w3.org/2000/svg" role="img" aria-label="Polyomino shape examples: 1-omino through 5-omino">
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<text x="35" y="62" text-anchor="middle" fill="white" font-size="24" font-weight="700">1</text>
<text x="35" y="105" text-anchor="middle" fill="#b388ff" font-size="12">1-omino</text>
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<rect x="140" y="30" width="50" height="50" rx="4" fill="#7c4dff" opacity="0.8"></rect>
<text x="115" y="62" text-anchor="middle" fill="white" font-size="24" font-weight="700">2</text>
<text x="165" y="62" text-anchor="middle" fill="white" font-size="24" font-weight="700">2</text>
<text x="140" y="105" text-anchor="middle" fill="#b388ff" font-size="12">domino</text>
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<rect x="220" y="70" width="40" height="40" rx="4" fill="#7c4dff" opacity="0.7"></rect>
<rect x="260" y="70" width="40" height="40" rx="4" fill="#7c4dff" opacity="0.7"></rect>
<text x="240" y="57" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="240" y="97" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="280" y="97" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="253" y="125" text-anchor="middle" fill="#b388ff" font-size="11">L-tromino</text>
<rect x="340" y="20" width="35" height="35" rx="4" fill="#7c4dff" opacity="0.6"></rect>
<rect x="375" y="20" width="35" height="35" rx="4" fill="#7c4dff" opacity="0.6"></rect>
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<text x="357" y="43" text-anchor="middle" fill="white" font-size="16" font-weight="700">4</text>
<text x="392" y="43" text-anchor="middle" fill="white" font-size="16" font-weight="700">4</text>
<text x="427" y="43" text-anchor="middle" fill="white" font-size="16" font-weight="700">4</text>
<text x="392" y="79" text-anchor="middle" fill="white" font-size="16" font-weight="700">4</text>
<text x="392" y="110" text-anchor="middle" fill="#b388ff" font-size="11">T-tetromino</text>
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<rect x="455" y="40" width="30" height="30" rx="3" fill="#7c4dff" opacity="0.5"></rect>
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<text x="470" y="30" text-anchor="middle" fill="white" font-size="14" font-weight="700">5</text>
<text x="470" y="60" text-anchor="middle" fill="white" font-size="14" font-weight="700">5</text>
<text x="500" y="60" text-anchor="middle" fill="white" font-size="14" font-weight="700">5</text>
<text x="500" y="90" text-anchor="middle" fill="white" font-size="14" font-weight="700">5</text>
<text x="500" y="120" text-anchor="middle" fill="white" font-size="14" font-weight="700">5</text>
</svg>
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<p>The key insight: <strong>a group of N can be any shape at all</strong>, as long as all N cells are orthogonally connected. A group of 5 is not limited to a straight 1×5 bar — it can bend, branch, and zigzag. This spatial freedom is what makes Fillomino richer than puzzles with fixed container shapes. Compare this to <a href="/guides/kakuro-number-crosswords/">Kakuro</a>, where runs are always straight horizontal or vertical lines — in Fillomino, your regions can go anywhere.</p>
<table class="comparison-table">
<thead>
<tr><th>Polyomino Size</th><th>Name</th><th>Possible Shapes</th><th>Example in Fillomino</th></tr>
</thead>
<tbody>
<tr><td>1</td><td>Monomino</td><td>1 shape (single cell)</td><td>A given clue of "1" is immediately complete</td></tr>
<tr><td>2</td><td>Domino</td><td>1 shape (straight pair)</td><td>Two adjacent 2s form a finished domino</td></tr>
<tr><td>3</td><td>Tromino</td><td>2 shapes (I, L)</td><td>Three 3s in a row or an L-bend</td></tr>
<tr><td>4</td><td>Tetromino</td><td>5 shapes (I, O, T, S, L)</td><td>Four 4s in any tetromino shape</td></tr>
<tr><td>5</td><td>Pentomino</td><td>12 shapes</td><td>Five 5s in any pentomino shape</td></tr>
<tr><td>6</td><td>Hexomino</td><td>35 shapes</td><td>Six 6s in any hexomino shape</td></tr>
<tr><td>7+</td><td>Heptomino+</td><td>108+ shapes</td><td>Large regions in hard puzzles wind freely</td></tr>
</tbody>
</table>
<h2 id="no-touch-rule">The No-Touch Principle: Fillomino's Most Powerful Constraint</h2>
<p>The no-touch rule (also called the no-merge rule) is deceptively simple: <strong>two separate groups with the same number cannot share an edge</strong>. This single rule generates most of the puzzle's deductive power. Let's see why with visual examples.</p>
<div class="fill-board">
<svg viewBox="0 0 400 200" xmlns="http://www.w3.org/2000/svg" role="img" aria-label="No-touch rule: orthogonal vs diagonal touching">
<text x="100" y="18" text-anchor="middle" fill="#ff5252" font-size="14" font-weight="700">✗ ILLEGAL — Orthogonal Touch</text>
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<text x="42" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="87" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="132" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
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<text x="87" y="109" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="87" y="145" text-anchor="middle" fill="#ff8a80" font-size="11">Two 3-groups share edge → merge to 4 cells = Rule 1 violation</text>
<text x="300" y="18" text-anchor="middle" fill="#69f0ae" font-size="14" font-weight="700">✓ LEGAL — Diagonal Touch</text>
<rect x="230" y="30" width="45" height="45" rx="4" fill="#7c4dff" opacity="0.8" stroke="#69f0ae" stroke-width="2"></rect>
<rect x="275" y="30" width="45" height="45" rx="4" fill="#7c4dff" opacity="0.8" stroke="#69f0ae" stroke-width="2"></rect>
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<text x="252" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="297" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="342" y="59" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
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<rect x="320" y="80" width="45" height="45" rx="4" fill="#7c4dff" opacity="0.8" stroke="#69f0ae" stroke-width="2"></rect>
<text x="342" y="109" text-anchor="middle" fill="white" font-size="20" font-weight="700">3</text>
<text x="300" y="145" text-anchor="middle" fill="#69f0ae" font-size="11">3-groups touch only at corner → legal, no merge</text>
<rect x="20" y="160" width="360" height="30" rx="6" fill="#263238"></rect>
<text x="200" y="180" text-anchor="middle" fill="#b388ff" font-size="12">Rule: same-number groups may touch diagonally (corner) but NOT orthogonally (edge)</text>
</svg>
</div>
<p>This rule creates <strong>invisible borders</strong> across the grid. When two separate 4 clues exist, you know their regions must eventually be separated by at least one cell of a different number on every orthogonal path between them. This lets you place borders preemptively — for example, if a cell between two 4 clues can only be reached by one of them (based on available space), that cell must belong to that 4's region, and the other 4's region must grow in a different direction.</p>
<h2 id="eight-techniques">8 Core Solving Techniques</h2>
<p>Every Fillomino puzzle, from easy 5×5 to expert 14×14, can be solved using these eight techniques in priority order. Master them in sequence — each technique builds on the previous ones.</p>
<div class="strategy-grid">
<div class="strategy-card">
<h3>① Complete the 1s</h3>
<p>A clue of 1 is already a finished group — one cell, one number. Immediately mentally (or with pencil marks) place borders on all four orthogonal neighbours. None of those neighbours can be 1.</p>
<p><strong>When to use:</strong> Always first. 1s are the fastest, most certain deductions in the puzzle.</p>
</div>
<div class="strategy-card">
<h3>② Merge Adjacent Same Numbers</h3>
<p>When two cells with the same number are orthogonally adjacent, they <em>must</em> belong to the same group. Two touching 4s are already two cells of a four-cell group — you need exactly 2 more connected cells for that group.</p>
<p><strong>When to use:</strong> After 1s. Scan for adjacent identical clues.</p>
</div>
<div class="strategy-card">
<h3>③ Forced Expansion</h3>
<p>When a clue has limited room to grow (blocked by grid edges, completed groups, or different-numbered clues), its expansion path is forced. A lone 3 in a corner can only extend in 2 directions — its possible shapes are heavily constrained.</p>
<p><strong>When to use:</strong> Whenever a clue has fewer expansion directions than cells it needs.</p>
</div>
<div class="strategy-card">
<h3>④ Count Cells in Enclosed Spaces</h3>
<p>When empty cells are surrounded by completed groups on most sides, count the remaining empty cells. If exactly N cells are enclosed, they must form a group of N — all filled with the number N.</p>
<p><strong>When to use:</strong> Whenever borders create isolated pockets of empty cells.</p>
</div>
<div class="strategy-card">
<h3>⑤ No-Touch Border Placement</h3>
<p>Two separate groups with the same number cannot share an edge. If placing a number in a cell would cause two same-number groups to become orthogonally adjacent, that placement is impossible — place a border instead.</p>
<p><strong>When to use:</strong> Whenever you see two separate clues with the same number nearby.</p>
</div>
<div class="strategy-card">
<h3>⑥ Region Growth Tracking</h3>
<p>For each incomplete group, track how many cells it still needs and which empty cells it can potentially reach. A group of 7 with 4 cells placed still needs 3 more cells — and those 3 must be orthogonally connected to the existing 4.</p>
<p><strong>When to use:</strong> Continuously throughout solving. Maintain a mental (or written) count for each group.</p>
</div>
<div class="strategy-card">
<h3>⑦ Introduce New Numbers</h3>
<p>Not every number in the solution appears as a given clue. When an enclosed pocket of empty cells has a definite count, fill them all with that count's number — even if it never appeared in the starting grid.</p>
<p><strong>When to use:</strong> When enclosed spaces have unambiguous cell counts.</p>
</div>
<div class="strategy-card">
<h3>⑧ Parity & Contradiction</h3>
<p>In hard puzzles, use parity arguments: if placing a number in cell X leads to an impossible situation elsewhere (two same-number groups forced to touch, or a group that cannot reach its required size), then cell X must contain a different number.</p>
<p><strong>When to use:</strong> When techniques ①-⑦ are exhausted on hard puzzles.</p>
</div>
</div>
<table class="comparison-table">
<thead>
<tr><th>Priority</th><th>Technique</th><th>Key Question to Ask</th><th>Cells Resolved</th></tr>
</thead>
<tbody>
<tr><td>①</td><td>Complete the 1s</td><td>"Is there a 1 clue? → Done."</td><td>1 cell per 1-clue</td></tr>
<tr><td>②</td><td>Merge adjacent same numbers</td><td>"Are two identical clues touching?"</td><td>2+ cells per merge</td></tr>
<tr><td>③</td><td>Forced expansion</td><td>"Can this clue only grow one way?"</td><td>1-3 cells per clue</td></tr>
<tr><td>④</td><td>Count enclosed cells</td><td>"How many empty cells in this pocket?"</td><td>All cells in pocket</td></tr>
<tr><td>⑤</td><td>No-touch border</td><td>"Would this placement merge two groups?"</td><td>1 border per deduction</td></tr>
<tr><td>⑥</td><td>Region growth tracking</td><td>"How many more cells does this group need?"</td><td>1-2 cells per step</td></tr>
<tr><td>⑦</td><td>Introduce new numbers</td><td>"Is this pocket's size a number not yet seen?"</td><td>All cells in pocket</td></tr>
<tr><td>⑧</td><td>Parity & contradiction</td><td>"If X goes here, does something break?"</td><td>1 cell per chain</td></tr>
</tbody>
</table>
<h2 id="worked-example">Worked 5×5 Example: Step by Step</h2>
<p>Let's walk through a real 5×5 Fillomino puzzle from start to finish. This example demonstrates how the first four techniques combine to solve an entire puzzle.</p>
<h3>Stage 1: The Starting Grid</h3>
<p>Here's our starting puzzle. The given clues are: a 2 in row 1 column 1, a 3 in row 2 column 3, a 1 in row 3 column 5, a 2 in row 4 column 2, and a 3 in row 5 column 4.</p>
<div class="fill-board">
<svg viewBox="0 0 300 300" xmlns="http://www.w3.org/2000/svg" role="img" aria-label="Fillomino 5x5 starting grid with clues">
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<text x="49" y="57" text-anchor="middle" fill="#b388ff" font-size="22" font-weight="700">2</text>
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<text x="153" y="109" text-anchor="middle" fill="#b388ff" font-size="22" font-weight="700">3</text>
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<text x="257" y="161" text-anchor="middle" fill="#b388ff" font-size="22" font-weight="700">1</text>
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<text x="101" y="213" text-anchor="middle" fill="#b388ff" font-size="22" font-weight="700">2</text>
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<text x="205" y="265" text-anchor="middle" fill="#b388ff" font-size="22" font-weight="700">3</text>
</svg>
</div>
<h3>Stage 2: Apply Technique ① — Complete the 1s</h3>
<p>The clue at R3C5 is a <span class="clue-example">1</span>. This cell is already a complete group. Its neighbours (R2C5, R4C5, R3C4) cannot be 1. We mark this as a finished single-cell region.</p>
<h3>Stage 3: Apply Technique ③ — Forced Expansion for 2s</h3>
<p>The clue at R1C1 is a <span class="clue-example">2</span>. It can only expand right (to R1C2) or down (to R2C1). Both cells must become 2 if this group uses them. Let's say we place it expanding downward: R1C1 and R2C1 both become 2. Similarly, R4C2's 2 can expand to R4C1, R4C3, R3C2, or R5C2 — we must check which placements avoid violating the no-touch rule with the other 2-clue.</p>
<h3>Stage 4: Apply Technique ⑤ — No-Touch Separation</h3>
<p>The two 3-clues at R2C3 and R5C4 must belong to separate three-cell groups. They cannot share an edge at any point. This means cells between them must contain different numbers, creating borders that help constrain other groups.</p>
<h3>Stage 5: Apply Technique ④ — Count Enclosed Cells</h3>
<p>As groups take shape, empty pockets form. Count the cells in each pocket: if a pocket has exactly N cells enclosed by completed borders, all N cells become the number N. This is often the technique that cracks the final sections of the puzzle open.</p>
<div class="info-box">
<h4>🎯 Key Takeaway from This Example</h4>
<p>Notice how we never guessed. Every placement was forced by one of the four basic techniques: complete 1s first, merge adjacent same-numbers, expand into forced paths, and count enclosed cells. The no-touch rule provided additional border information. On a 5×5 grid with many clues, these four techniques are usually sufficient. On larger or sparser grids, techniques ⑥-⑧ (growth tracking, new number introduction, parity) kick in for the harder deductions.</p>
</div>
<h2 id="advanced-strategies">Advanced Strategies for Hard Puzzles</h2>
<p>Once you master the eight core techniques, these advanced strategies help on larger grids (10×10 and above) where deduction chains grow longer.</p>
<div class="technique-box">
<h4>🔗 Chain Deduction: "If This Group Goes Here, Then..."</h4>
<p>On hard puzzles, a single placement often triggers a cascade. Place a 3 → it borders a 5-clue → the 5 can only expand left → the cells to the left form a pocket of 4 → those 4 cells must all be 4 → that 4-group borders another clue... Learn to follow these chains two or three steps ahead. Write small pencil marks for cells you're confident about but haven't fully confirmed.</p>
</div>
<div class="technique-box">
<h4>📐 Boundary Compression</h4>
<p>When two large-number clues (say 7 and 8) are near each other, their regions compete for space. If the available cells between and around them are limited, the shapes become heavily constrained. A 7-clue needs seven cells — if only 8 cells are reachable, the group must occupy 7 of those 8, and the remaining 1 cell belongs to a different group. This "compression" effect dramatically narrows possibilities.</p>
</div>
<div class="technique-box">
<h4>🔄 Region Counting (Sum Check)</h4>
<p>Count the total cells in the grid (rows × columns). Then sum all given clues. The difference tells you how many cells belong to groups that have no given clues at all. For example, in a 7×7 grid (49 cells) with givens summing to 30, there are 19 cells in groups without clues. This information helps you estimate how many new numbers need to be introduced and how large the "hidden" regions must be.</p>
</div>
<div class="technique-box">
<h4>⚡ Parity Arguments</h4>
<p>In advanced puzzles, you may encounter situations where placing number X in cell A leads to an even-sized pocket elsewhere — but even pockets cannot be filled by a single group (because groups must have the same number as their size, and the parity doesn't work out). These parity constraints are rare but powerful when they apply. They typically appear in 10×10+ grids with sparse clues.</p>
</div>
<h2 id="comparison">Fillomino vs Other Logic Puzzles</h2>
<p>Fillomino occupies a unique niche among logic puzzles. Here's how it compares to other popular types on our site:</p>
<table class="comparison-table">
<thead>
<tr><th>Feature</th><th>Fillomino</th><th>Nonogram</th><th>Sudoku</th><th>Kakuro</th><th>Nurikabe</th><th>Shikaku</th></tr>
</thead>
<tbody>
<tr><td><strong>Core mechanic</strong></td><td>Grow numbered regions</td><td>Fill/empty from edge clues</td><td>Place digits in fixed boxes</td><td>Sum digits in runs</td><td>Separate islands from sea</td><td>Draw rectangles around clues</td></tr>
<tr><td><strong>Region shapes</strong></td><td>Any polyomino (flexible)</td><td>Fixed rows/columns</td><td>Fixed 3×3 boxes</td><td>Straight runs</td><td>Rectangular islands</td><td>Any rectangle</td></tr>
<tr><td><strong>Spatial reasoning</strong></td><td>⭐⭐⭐⭐⭐ High</td><td>⭐⭐⭐ Medium</td><td>⭐⭐ Low</td><td>⭐⭐ Low</td><td>⭐⭐⭐⭐ High</td><td>⭐⭐⭐⭐ High</td></tr>
<tr><td><strong>Number logic</strong></td><td>⭐⭐⭐⭐ High</td><td>⭐⭐ Low</td><td>⭐⭐⭐⭐ High</td><td>⭐⭐⭐⭐⭐ Highest</td><td>⭐ Low</td><td>⭐⭐ Low</td></tr>
<tr><td><strong>Unique constraint</strong></td><td>No-touch / no-merge</td><td>Overlap / edge logic</td><td>Row/col/box uniqueness</td><td>Sum targets</td><td>White cells connected</td><td>Area = clue number</td></tr>
<tr><td><strong>Best for fans of</strong></td><td>Shape-building + numbers</td><td>Picture revelation</td><td>Pure digit placement</td><td>Mental arithmetic</td><td>Island growing</td><td>Rectangle fitting</td></tr>
</tbody>
</table>
<p>If you enjoy the spatial reasoning of <a href="/guides/nurikabe-island-puzzle-rules/">Nurikabe</a> (growing islands in a sea of black cells) but want to add number logic, Fillomino is a natural next step. If you like <a href="/guides/shikaku-rectangle-puzzles/">Shikaku</a> (dividing a grid into rectangles matching clue numbers), Fillomino offers the same region-building satisfaction but with flexible polyomino shapes instead of rigid rectangles. For fans of <a href="/guides/akari-lightbulb-puzzle-strategy/">Akari</a> or <a href="/guides/hashiwokakero-bridge-puzzles/">Hashiwokakero</a>, Fillomino shares the "grow regions from clues" mechanic but adds the no-touch constraint that creates its distinctive deductive character.</p>
<p>Fillomino also pairs well with <a href="/guides/nonogram-picross-puzzles-guide/">Nonogram</a> (both use grid-filling logic but from completely different angles) and <a href="/guides/kakuro-number-crosswords/">Kakuro</a> (both feature number placement, but Kakuro's runs are straight while Fillomino's regions can bend freely). If you want a puzzle that combines spatial and numerical reasoning in equal measure, Fillomino sits at the sweet spot — check out our <a href="/guides/math-puzzles-for-kids-and-adults/">math puzzles guide</a> for more number-based brain training options.</p>
<h2 id="faq">Frequently Asked Questions</h2>
<div class="strategy-card" style="margin-bottom: 1rem;">
<h3>Can Fillomino regions be non-rectangular?</h3>
<p>Absolutely. In fact, most Fillomino regions <em>are</em> non-rectangular. A group of 5 can be any of the 12 possible pentomino shapes (L, T, S, Z, I, P, F, W, U, V, X, Y). The only requirement is that all cells in a group are orthogonally connected. Rectangular groups happen when the puzzle's clues force a straight or box-like arrangement, but on larger grids, regions wind and bend freely.</p>
</div>
<div class="strategy-card" style="margin-bottom: 1rem;">
<h3>What happens if two same-number groups accidentally touch?</h3>
<p>That's a rule violation — two separate groups with the same number sharing an edge would merge into one larger group, which then violates the size-matching rule (the merged group has too many cells). In practice, if you notice this happening while solving, it means one of the groups must be rerouted: some cells need to change their number to break the unwanted connection. The no-touch rule is your primary diagnostic tool for catching mistakes early.</p>
</div>
<div class="strategy-card" style="margin-bottom: 1rem;">
<h3>How is Fillomino different from Shikaku?</h3>
<p>Both puzzles involve dividing a grid into regions matching clue numbers, but with a key difference: <a href="/guides/shikaku-rectangle-puzzles/">Shikaku</a> requires every region to be a <strong>rectangle</strong>, while Fillomino allows <strong>any polyomino shape</strong>. Shikaku is purely about rectangle-fitting (the clue tells you the area, not a digit to repeat). Fillomino requires you to fill every cell with the region's number and manage the no-touch constraint. Shikaku tends to be more geometric; Fillomino more spatially creative.</p>
</div>
<div class="strategy-card" style="margin-bottom: 1rem;">
<h3>Is there a mobile app for Fillomino?</h3>
<p>Yes. The mobile game <strong>Fields</strong> (iOS, released 2013) offers a polished Fillomino experience. Several web-based platforms also host Fillomino puzzles, including logic-puzzles-online.com, gridpuzzle.com, and Nikoli's own puzzle collection. Most digital implementations include features like error checking, hint systems, and multiple grid sizes (5×5 through 14×14).</p>
</div>
<section class="related-guides" style="margin-top: 2rem; padding: 1.5rem; background: var(--card-bg, #f8f9fa); border-radius: 10px;">
<h2>Related Puzzle Guides</h2>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(200px, 1fr)); gap: 0.75rem;">
<a href="/guides/nonogram-picross-puzzles-guide/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Nonogram (Picross) Guide →</a>
<a href="/guides/nurikabe-island-puzzle-rules/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Nurikabe Island Puzzle →</a>
<a href="/guides/shikaku-rectangle-puzzles/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Shikaku Rectangles →</a>
<a href="/guides/kakuro-number-crosswords/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Kakuro Number Crosswords →</a>
<a href="/guides/akari-lightbulb-puzzle-strategy/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Akari Light Bulb →</a>
<a href="/guides/hashiwokakero-bridge-puzzles/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Hashiwokakero Bridges →</a>
<a href="/guides/yinyang-circular-puzzle-guide/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Yin-Yang Circular →</a>
<a href="/guides/masyu-pearl-loop-puzzle-guide/" style="padding: 0.75rem; background: white; border-radius: 8px; text-decoration: none; color: var(--accent, #7c4dff);">Masyu Pearl Loop →</a>
</div>
</section>