Shikaku puzzle solved step by step
A Shikaku puzzle is a grid with numbers scattered through it, and the whole job is to cut that grid into rectangles. It takes about thirty seconds to learn and rather longer to get good at, and the gap between those two is where most people give up. This page closes it with one board. Below is an original 7×7 puzzle, then the first seven rectangles worked out in order with the reason each one is forced, then the finished grid. The word Shikaku is ordinary Japanese with several unrelated senses, so a plain search mixes puzzle pages with material about qualifications and eyesight; this page means the grid puzzle. For the rules in general terms, along with solving tips and the shape-glyph variation, see what is Shikaku.
The rule, in three lines
Divide the whole grid into rectangles. Every cell ends up inside exactly one rectangle. Each rectangle contains exactly one number, and that number is how many cells the rectangle covers.
That is the entire game. A square counts as a rectangle, so a 4 can be a 2×2. A single cell counts too, so a 1 is a rectangle all by itself. The numbers always add up to the number of cells in the grid, which is the first thing worth checking on any board you are handed: a 7×7 grid holds 49 cells, so its clues total 49.
Reading a number
A clue tells you the area. The factor pairs of that area tell you the shapes, and the grid tells you which of those shapes can physically fit. On a board seven cells wide and seven cells tall, that pruning starts early.
| Clue | Shapes that fit a 7×7 board |
|---|---|
| 1 | 1×1 |
| 2 | 1×2, 2×1 |
| 3 | 1×3, 3×1 |
| 4 | 1×4, 4×1, 2×2 |
| 5 | 1×5, 5×1 |
| 6 | 1×6, 6×1, 2×3, 3×2 |
| 7 | 1×7, 7×1 |
| 8 | 2×4, 4×2 |
| 9 | 3×3 |
| 10 | 2×5, 5×2 |
| 12 | 2×6, 6×2, 3×4, 4×3 |
Two of those rows do a lot of work. A prime clue has only the two thin shapes, which makes it easy to place and easy to block with. And a 9 on a board this size has exactly one shape, because a 1×9 strip has nowhere to go — the clue is half-solved the moment you read it.
The second thing a clue tells you is where it cannot go. A rectangle holds exactly one number, so any rectangle that would swallow a second clue is dead on arrival. On a crowded board that rule eliminates more candidates than the arithmetic does.
The puzzle
Rows are numbered from the top, columns from the left, so r4c5 is the fourth row, fifth column. Blank cells are yours to claim.
Eleven clues: 4, 4, 2, 6, 2, 8, 3, 6, 2, 4, 8. They total 49, which is the cell count, so the board is at least arithmetically honest. Solve it before reading on if you like — the rest of this page is the answer.
Solving it, one rectangle at a time
Every step below is forced. Nothing is guessed, nothing is tried and undone.
1. The top-left corner. Ask which clue can reach r1c1 — not which clue you would like to put there. The 2 at r4c1 covers two cells, so it cannot stretch three rows up. The 4 at r2c4 would have to span columns 1 to 4 and rows 1 to 2 to hold both cells, which is eight cells, not four. That leaves the 4 at r1c3, and only one of its three shapes works: the upright 1×4 stays inside column 3, and a 2×2 would need three columns to span c1 and c3, so it has to be the flat 4×1 strip along row 1, columns 1 to 4. Row 1, columns 1-4.
2. Down the column from r1c5. The strip just placed stops at column 4, so r1c5 is still open and something has to cover it. The 2 at r2c5 can, as a vertical pair. Can anything else? Every 6-shape from r2c6 that reaches r1c5 also passes through r2c5, and r2c5 is a clue, so those are all dead. The same objection kills the 2×2 that the 4 at r2c4 would need. And an 8 is 2×4 or 4×2 on this board — neither reaches from r4c5 to row 1 without swallowing a clue on the way. Rows 1-2, column 5.
3. The top-right corner. Only the 6 at r2c6 is near enough to cover r1c7 — the other 8 sits four rows below it. Of the 6’s four shapes, the 1×6 runs down column 6 and stops short of column 7, the flat 6×1 lies inside row 2, and the 3×2 lying across columns 5 to 7 would take r2c5, which is spoken for and is a clue besides. So the 6 stands upright: two columns wide, three rows tall, columns 6 and 7, rows 1 to 3. Rows 1-3, columns 6-7.
4. The 8 in the middle. An 8 on a seven-row board is 2×4 or 4×2, and this one sits at r4c5. Work through the six placements of a 4×2: across rows 3 and 4 it can start at column 2, 3 or 4, and the last two run into cells the 6 already owns. Across rows 4 and 5 all three placements pick up a second clue — the 3 at r5c2, the 6 at r5c5, or both. The upright 2×4 versions fare no better; every one of them either crosses the cells taken in steps 1 to 3 or contains the 6 at r5c5. One placement survives. Rows 3-4, columns 2-5.
5. The second row. Now look back at the 4 at r2c4. Its upright 1×4 down column 4 needs r3c4 and r4c4, which the 8 has just taken. Its 2×2 options need row 1 or row 3, both gone. Sliding the flat 4×1 one step right needs r2c5, which is gone. What is left is the strip along row 2, columns 1 to 4 — directly under the first rectangle you placed. Row 2, columns 1-4.
6. Back to the left edge. Cell r3c1 is open and only the 2 at r4c1 is close enough to claim it. That 2 had three placements: up into r3c1, down into r5c1, or sideways into r4c2. The 8 took r4c2 in step 4, and the downward pair leaves r3c1 with no clue that can ever reach it. Rows 3-4, column 1.
7. The right-hand column pair. Cell r4c6 is open. The 6 at r5c5 would have to swallow the 8’s own cell at r4c5 to reach row 4 at all, so the only clue left on that side is the 8 at r7c6. Of its two placements — upright across columns 6 and 7, or flat across rows 6 and 7 — only the upright one touches r4c6. Rows 4-7, columns 6-7.
The last four fall out in sequence. With columns 6 and 7 closed, the 6 at r5c5 has one shape left: two columns wide, three rows tall, columns 4 and 5, rows 5 to 7. That leaves a 3×3 block in the bottom-left holding exactly three clues — a 3, a 2 and a 4, totalling nine cells. The 4 must be the 2×2 in the lower corner of that block, because the higher 2×2 would take the 3’s own cell. The 3 then runs flat along row 5, and the 2 takes what remains of column 1.
The finished grid
The figure shows every rectangle outlined, with a letter in each cell and the clue number still visible where it was printed.
| Rectangle | Clue | Shape | Rows | Columns |
|---|---|---|---|---|
| A | 4 | 4 wide x 1 tall | 1 | 1-4 |
| B | 2 | 1 wide x 2 tall | 1-2 | 5 |
| C | 6 | 2 wide x 3 tall | 1-3 | 6-7 |
| D | 4 | 4 wide x 1 tall | 2 | 1-4 |
| E | 2 | 1 wide x 2 tall | 3-4 | 1 |
| F | 8 | 4 wide x 2 tall | 3-4 | 2-5 |
| G | 8 | 2 wide x 4 tall | 4-7 | 6-7 |
| H | 3 | 3 wide x 1 tall | 5 | 1-3 |
| I | 6 | 2 wide x 3 tall | 5-7 | 4-5 |
| J | 2 | 1 wide x 2 tall | 6-7 | 1 |
| K | 4 | 2 wide x 2 tall | 6-7 | 2-3 |
Eleven rectangles, 49 cells, each clue matching the area of the shape it sits in. This board has exactly one solution, and every rectangle above was placed by elimination rather than by trial.
Four habits that carry most boards
Start where the grid is tight, not where the clues are. Corners and edges have the fewest clues within reach, which is why step 1 worked before anything else did. A corner cell often has one possible owner on a board where no clue yet has one possible shape.
Count the shapes before you count anything else. Write the factor pairs of a clue in the margin and strike the ones the grid edge forbids. A clue down to one shape is a rectangle you can ink in, and it usually takes two or three neighbours with it.
Use clues as walls. A rectangle holds one number, so every other number on the board is a barrier. Most of the eliminations on this page came from that rule rather than from arithmetic — half the placements died because they would have swallowed a second clue.
Re-read the neighbours after every placement. Fixing one rectangle changes what the clues around it can still do, which is what turned steps 4 and 5 and the whole closing sequence from open questions into single options. Shikaku cascades; a board that looked stuck two moves ago usually opens.
Where the boards come from
A puzzle like the one above is quick to solve and slow to build by hand, because the awkward part is the guarantee — proving that one answer exists and one only. Shikaku is the Puzzle Maker Pro module that does that work. Grids run from 4×4 up to 20×20 and open at 7×7, with a Lock to square tick that keeps both axes together until you untick it. Ensure unique solution is on out of the box, which is the setting that makes a printed board behave like the one on this page. A Larger areas dial biases the generator toward bigger rectangles and thinner clue counts, and Quantity takes up to a hundred boards in a run.
Two choices decide how the pages look. The puzzle prints its clues as Numbers, in the classic form used above, or as Patches — shape glyphs, or your own images, that tell the solver whether a rectangle is square, wide or tall instead of naming its area. The answer page draws the rectangles as region borders or fills each one with its own colour. Pages export as JPG, PNG, transparent PNG or SVG, puzzle and key together.
The walkthroughs are on the site: creating your first Shikaku puzzle, styling the grid, the Patches and colour-hint modes, batching a run and assembling the result into a book. They all sit under Shikaku tutorials.
The whole point
The rule is one sentence and the technique is four habits. Ask which clue can reach a given cell rather than which cell a clue would like; strike the shapes the grid edge forbids; treat every other number as a wall; and read the neighbourhood again after each rectangle lands. The board above yields to that and nothing else, from the top-left corner to the last pair of cells in column 1.