How to Solve Patches & Shikaku: 7 Techniques

Shikaku puzzles, and their modern cousins like LinkedIn's Patches and our own Plots, have rules a child can follow: cut the grid into rectangles, one number in each, with the number equal to the area. Yet a well-made board can stop an experienced solver in their tracks. The difference between a slow solve and a fast one isn't speed of hand. It's knowing where to look. These seven techniques work for any Shikaku-style puzzle, with or without shape hints.

The rules, briefly

• Divide the entire grid into rectangles. Squares are rectangles too.
• Each rectangle contains exactly one number.
• The number equals the rectangle's area (a 6 covers six cells).
• When a shape hint is shown, the rectangle must be a square, wider than tall, or taller than wide, as indicated.

Every Plots board has exactly one solution, checked by a solver before it's served, so every step below is pure deduction.

Technique 1: List the possible shapes for each number

Start by thinking in factors. Each number can only form rectangles whose sides multiply to it:

• 1: a single cell.
• 2, 3, 5, 7: prime numbers, so only straight lines (1×2, 1×3, 1×5, 1×7), either across or down.
• 4: a 1×4 line or a 2×2 square.
• 6: a 1×6 line or a 2×3 block, either way round.
• 8: a 1×8 line or a 2×4 block.
• 9: a 1×9 line or a 3×3 square.
• 10: a 1×10 line or a 2×5 block.

With a shape hint, the list gets even shorter. A "square" 4 must be 2×2, and a "wide" 6 is either 1 row by 6 columns or 2 rows by 3 columns. On a 6×6 board, that "wide" 6 can't be 1×6 unless its whole row is otherwise empty, so it's often forced to be 2×3.

Technique 2: Slide each shape around its number

A shape can sit in several positions and still cover its number. A 1×3 line through a cell can have that cell at its left end, middle or right end. For each number, picture every position of every allowed shape, then cross out the ones that:

• run off the edge of the grid,
• cover another number,
• overlap a rectangle you've already placed.

Often only one position survives. That's a rectangle you can draw right away. Numbers in corners and against edges are the best place to start, because the grid boundary rules out so many positions.

Technique 3: Find each empty cell's owner

Flip the question around. Instead of asking where a number's rectangle can go, pick an empty cell and ask which numbers could possibly reach it. If only one number can, that cell belongs to that number's rectangle.

This is the most powerful technique on harder boards. A lonely cell tucked behind other clues often has just one possible owner, and once you know the rectangle must include it, the rectangle's size and position are usually fixed too.

Technique 4: Big numbers in tight spaces

Large numbers are your friends early on. A 9 near a corner of a 6×6 board can't be a straight 1×9 line (it wouldn't fit), so it must be a 3×3 square, and there are only a few places a 3×3 square can sit around its number without hitting the edge or another clue.

On the other hand, small numbers in wide-open areas are often the last to be solved. Leave them for later. Once the big rectangles are drawn, the small ones usually have only one place left.

Prefer paper?

Paperback · Adults

Star Battle & Takuzu

120 Logic Puzzles for Adults, Warm-Up to Expert

The paper versions of Queens and Tango: one star per row, column and region, and balanced grids of ● and ○. Big 6.6-inch grids, one puzzle per page.

• ✓120 puzzles, each with exactly one solution
• ✓3 levels: Warm-Up, Challenge, Expert
• ✓Rules, worked examples and full solutions

Get it on Amazon

Technique 5: Use the shape hints

When a puzzle shows shape hints, read them as strict rules:

• Square: the width equals the height. A square 4 is 2×2, a square 9 is 3×3. A number that isn't a perfect square (like 6) will never carry a square hint.
• Wide: more columns than rows. A wide 2 is two cells side by side.
• Tall: more rows than columns. A tall 3 is three cells stacked.

In Plots, Normal boards show a hint for every number, which makes Technique 1 very fast. Hard boards hide most hints, so you'll lean on Techniques 2 and 3 instead.

Technique 6: Watch the leftover areas

Every time you draw a rectangle, look at the empty space around it. If you've left a small pocket of cells, count them and look at the numbers inside. A pocket of four cells containing a single 4 must be exactly that rectangle, if the pocket's shape allows it. A pocket of three cells containing a 4 means something went wrong: one of your rectangles is in the wrong place.

This counting check works the other way too. When choosing between two positions for a rectangle, see which one leaves the neighbouring space in a shape the remaining numbers can actually fill.

Technique 7: Don't be afraid to redraw

In Plots, drawing a rectangle over existing ones replaces them, and tapping a rectangle removes it, so experimenting is cheap. Rectangles that don't satisfy their clue are shown with a dashed red outline, which makes mistakes easy to spot.

Still, the best habit is to draw only what you've proven. If you catch yourself guessing, stop and go back to Technique 3: find a cell with a single possible owner. There's always one somewhere on a well-made board.

A worked example

Here's how these techniques combine on a real situation. Imagine a 6×6 board with a 9 one cell in from the top-left corner: row 2, column 2.

A 9 is either a 1×9 line or a 3×3 square. A 1×9 line can't fit in a grid only six cells wide, so this rectangle must be a 3×3 square (Technique 1 and Technique 4 together). The square has to contain row 2, column 2, which leaves four possible positions: covering rows 1–3 or rows 2–4, and columns 1–3 or columns 2–4.

Now suppose there's a 2 at row 4, column 3. Both squares that cover rows 2–4 would include that cell, and a rectangle can only hold one number. So the 9 must cover rows 1–3 (Technique 2).

Finally, suppose there's a 3 at row 1, column 4. The square covering columns 2–4 would swallow it, so that position is out too. Only one position is left: rows 1–3, columns 1–3. Three clues, three quick deductions, and a nine-cell rectangle is placed without any guessing. On a real board you'll do this kind of reasoning dozens of times, and it gets faster every time.

A routine for every board

1. 1Draw any 1s and any number whose rectangle has only one possible position.
2. 2Handle big numbers near corners and edges.
3. 3Use shape hints to cut down each number's options.
4. 4Look for empty cells with a single possible owner.
5. 5After each rectangle, check the leftover pockets.
6. 6Repeat until the board is full.

Practise on paper

Shikaku is a classic pencil puzzle, and it's lovely to solve on paper. Our free printable pack has 12 Plots puzzles: six 6×6 boards with shape hints and six 8×8 boards with most hints hidden, plus every solution.

Free printables

Free printable puzzle packs

Print-ready PDFs with the rules, 10 to 12 puzzles and every answer. Tick as many packs as you like, and print as many copies as you want for home or the classroom.

Choose your packs

Star Battle & Takuzu12 puzzles · AdultsLogic Puzzles for Kids12 puzzles · Kids 6–10Funny & Witty Cryptograms10 puzzles · Word loversInspirational Cryptograms10 puzzles · Word loversSudoku12 puzzles · Easy to MediumTrail path puzzles12 puzzles · Like LinkedIn ZipPlots (Shikaku)12 puzzles · Like LinkedIn Patches

Send me the PDFs

Yes, email me occasional new printables and offers for Puzzle Theory books on Amazon. Optional; unsubscribe anytime.

We'll save your email and chosen packs and email the PDF links. Book offers are only sent if you opt in above. This does not sign you up for the daily puzzle newsletter.

Practise as much as you like

Shikaku skills grow fast with practice, and Plots makes that easy: there's a daily board for everyone, plus unlimited practice boards, each one checked to have exactly one solution. Start on Normal (6×6, every shape shown) to learn the patterns, then move to Hard (8×8, most shapes hidden) when the hints start to feel like training wheels.

Want to know how Plots compares with LinkedIn's version? Read our Patches alternative guide. And if you enjoy grid logic, Trail is a path puzzle in the style of LinkedIn's Zip, with its own solving tips.