Single-Candidate Elimination: Regions Early, Rows Late
Single-candidate elimination is the one technique every Meowdoku player already uses, whether or not they have a name for it: a row, column or region with exactly one legal cell left is a cat, no further reasoning required. The opening-moves article on this site measured which of the three finds that one cell most often right after the free cats land, and regions won by a wide margin. That was one snapshot. Followed all the way through a solve, the picture is sharper than that snapshot suggested — and it tells you something the opening alone cannot: when each view is worth checking.
What single-candidate elimination is
A row, column or region is a container that must hold exactly one cat. Cross out every cell a container cannot legally use, and if only one cell survives, that cell is a cat — nothing about the rest of the board needs to be considered. It is the same idea sudoku calls a "naked single", applied to three kinds of container instead of two.
The mechanics are identical for all three: count the container’s still-legal cells, and if the count is one, place the cat there. Nothing about the technique privileges rows over regions or regions over columns. What differs, and what the rest of this article measures, is simply how often and how early each kind of container actually gets there.
The full picture, not just the opening
The opening-moves article asked one question: right after the free cats are placed, which kind of container is most likely to already be down to one candidate? Regions won clearly — on a Hard board, 12% of open regions were forced at that exact moment, against 0.7% of open rows.
That answers what to check first. It does not answer what to check fifth, or tenth, or in the endgame. To get that, this article runs single-candidate elimination all the way through — placing every forced cat it finds, then rescanning, over and over, until no row, column or region has just one legal cell left — and records which kind of container produced each cat along the way, and how many cats were already on the board when it fired.
Regions do most of the work, start to finish
Across four hundred boards per difficulty, run to the point where elimination stalls, here is which kind of container produced each forced cat over the entire trajectory, not just the opening:
| Board | From rows | From columns | From regions |
|---|---|---|---|
| Easy 5×5 | 31% | 31% | 38% |
| Normal 7×7 | 20% | 20% | 60% |
| Hard 9×9 | 15% | 15% | 69% |
| Extreme 10×10 | 5% | 6% | 89% |
Rows and columns split the remainder almost exactly evenly at every difficulty, which is expected — nothing about this ruleset favors one over the other, they are the same shape rotated ninety degrees. What is not symmetric is their share against regions, and the gap widens every time the board grows a size.
Rows and columns are an endgame tool
The share alone undersells how lopsided the timing is. For every forced cat, record how many cats were already on the board when that deduction became available:
| Board | Rows | Columns | Regions | Board size |
|---|---|---|---|---|
| Easy 5×5 | 2.9 | 2.9 | 2.7 | 5 |
| Normal 7×7 | 4.5 | 4.5 | 3.4 | 7 |
| Hard 9×9 | 6.6 | 6.5 | 4.5 | 9 |
| Extreme 10×10 | 8.0 | 7.6 | 3.3 | 10 |
On Extreme, a row-forced cat shows up with an average of eight of ten cats already down — the second-to-last cat on the board, typically. A region-forced cat shows up at 3.3, not even a third of the way through. As a share of the game, region deductions drift earlier as boards grow — from about half the way through on Easy to a third of the way through on Extreme — while row and column deductions drift later, from just over half the way through to four-fifths.
Why regions go first and rows go last
A region can start the game small. Nothing stops a region from having two or three cells to begin with, so it can be forced after a single nearby placement removes the rest. A row or column cannot start small — it always has exactly the board’s full width, and no single elimination technique shrinks it by more than a cell or two at a time.
A cat placed anywhere on the board removes exactly one cell from almost every other row and every other column: the cell in its own column, one per row. To force some other row down from N cells to one, elimination needs to have removed N − 1 of its cells — which, one placement at a time, takes most of a solved board’s worth of other cats. A region carries no such floor. That is the entire reason rows and columns are a late-game signal and regions are not: it is baked into how large a row starts, not into anything about the reasoning itself.
Where the three views actually compete
Easy 5×5 is the one board where this stops being lopsided. Rows and columns together account for 62% of all single-candidate deductions there, against 38% for regions — regions still lead individually, but not by the kind of margin seen from Normal upward. The opening-moves article flagged the same thing about the fresh board alone: "only on the 5×5 board do the three genuinely compete." This article confirms it holds for the whole game, not just the first move.
The reason is the same one section five just gave, run in reverse. A 5×5 region rarely starts much smaller than a row of five cells, so the size gap that makes bigger boards lopsided barely exists here. Habits built on Easy — where checking a row is nearly as productive as checking a region — are exactly the habits that mislead on Hard and Extreme.
What the in-game Hint button actually shows you
The Hint feature looks for the same three kinds of forced cell this article measures, but it does not treat them symmetrically: it checks every row before it checks any column, and every column before it checks any region, returning the first one it finds. When a row-forced cell and a region-forced cell are both sitting on the board at once, Hint shows the row.
That is a reasonable way to build a hint button — a player asking for help usually just wants a legal next move, not a lecture on which technique produced it. But it means Hint is not a representative sample of what actually happens during a solve. Lean on it to learn the game’s patterns and it will show you, disproportionately, the rarer and later-firing technique: the tables above are what elimination actually favors when every container is checked without a preference order.
A checklist for which view to check, and when
The practical version of all four tables above:
- Regions, the whole game. They account for the majority of single-candidate deductions on every board 7×7 and up, and they fire throughout the solve, not just at the start.
- Rows and columns, once the board is most of the way full. On Hard and Extreme they rarely have anything to offer before six or more of the cats are already down. Checking them earlier mostly wastes a scan.
- On Easy, check all three. The board is small enough that rows and columns pull close to even with regions, so there is no real shortcut to skip.
- Do not read Hint as a technique ranking. It shows the first forced cell in row-column-region order, not the most common one — use the tables above for that instead.
How this was measured
Both tables come from the game’s own generator, run across four hundred fresh boards at each of the four difficulties. Starting from the opening — the starter cat plus every one-cell region, exactly as the earlier article defines it — each board is solved by repeatedly finding every row, column and region with exactly one legal cell left, placing all of them, and rescanning, until nothing is forced. Every such event is logged with its container type and how many cats were already on the board at that moment; ties, where a single cell is the last candidate in more than one container at once, are simply counted under every container type that reached it.
These are properties of the boards this generator currently produces. The test suite that ships with this article re-derives both tables from freshly generated boards on every run, so a future retune of region sizing fails the build instead of leaving a stale statistic live on the page.
Try it stage by stage
Start a Hard 9×9. For the first half of the board, check regions only and see how far that alone takes you. Only start sweeping rows and columns once six or seven cats are down — that is where, on average, they actually start paying off.
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