☠️ Deadly Rectangle
A deadly rectangle is a situation where four cells form a perfect 2×2 block, all containing the same two candidates (say, 3 and 7).
If you don’t do anything about it, those cells could be filled in two different ways,one version has 3s and 7s swapped diagonally, and both versions would make a valid Sudoku solution.
That’s a big no-no, because a proper Sudoku has only one unique solution.
When a deadly rectangle can form, the puzzle becomes ambiguous.
“Unique Rectangle” rules exist to prevent that by letting you spot and eliminate candidates that could cause the deadly rectangle.
Summary of All Unique Rectangle Types
| Type | What Makes It Special | What You Do |
|---|---|---|
| 1 | One corner has an extra | That extra must be true |
| 2 | Two corners share the same extra | Eliminate that extra elsewhere |
| 3 | Two corners have different extras that interact | Eliminate those extras from shared houses |
| 4 | One corner’s extra forms a strong link | That extra is the answer |
| 5 | Two corners’ extras are strongly linked elsewhere | Use that link to make eliminations or force one true |
| 6 | Both base digits form strong links elsewhere | Use both links together to eliminate or force values |
1️⃣ Unique Rectangle Type 1
A Unique Rectangle Type 1 is a pattern used to prevent a deadly rectangle, a situation that could give the puzzle two possible solutions.
Here’s how it works:
You find four cells that could form a rectangle shape.
Three of those cells contain only two candidates (like 3 and 7).
The fourth cell has those same two candidates plus at least one extra number.
Now, if that extra number weren’t there, the four cells would make a deadly rectangle, meaning the puzzle would have two valid solutions. That can’t happen, so Sudoku logic tells us the extra candidate must be correct in that cell.
Once you realize that, you can safely:
Eliminate the two rectangle candidates (like 3 and 7) from that cell.
And if only one extra candidate remains, you can fill it in immediately, it’s guaranteed to be the right number.
2️⃣ Unique Rectangle Type 2
A Unique Rectangle Type 2 is another way to stop a deadly rectangle (the two-solution trap).
It’s similar to Type 1, but instead of one cell having extra candidates, now two cells in the same row or column have the extras.
How it works:
You spot four cells forming a rectangle.
All four share the same two candidates (say, 3 and 7).
But in this case, two of those cells (on the same row or column) also have one or more extra candidates, like 3, 7, and 9.
Now here’s the key:
If the two cells with the extras both ended up being 3 or 7, that would complete the deadly rectangle and cause multiple solutions, not allowed.
To avoid that, at least one of those extra candidates must be correct in one of those two cells. That means you can use that logic to eliminate the same extra candidate (like the 9) from other cells in the same row or column outside the rectangle.
3️⃣ Unique Rectangle Type 3
A Unique Rectangle Type 3 is another pattern that prevents a deadly rectangle (the two-solution trap), but this time, the “extra” candidates in the rectangle are connected to outside cells through a shared house (row, column, or box).
It’s like Type 2’s more strategic cousin, instead of just eliminating in the same row or column, you use interactions with other cells to make eliminations.
How it works:
You find four cells that could form a rectangle, all sharing the same two candidates (say 3 and 7).
Two of those cells (on one side of the rectangle) each have extra candidates, but not the same extras this time. For example:
One has 3, 7, 9
The other has 3, 7, 8
Those “extra” candidates (8 and 9) are both restricted to the same box, row, or column, they “see” each other.
If both those cells became 3 or 7, the puzzle would have two solutions (deadly rectangle). So we know that one of the extra candidates (8 or 9) must be true in one of those cells.
That means any other cells in that shared house that also contain 8 or 9 can’t have them, because one of those two cells must take it.
4️⃣ Unique Rectangle Type 4
A Unique Rectangle Type 4 is a situation where the puzzle would form a deadly rectangle, unless one of the “extra” candidates in a corner cell is forced to be true because of a strong link (a pair of cells where one must be true).
So, unlike Types 1–3, where you’re mostly eliminating candidates, Type 4 uses logic about what must happen due to that strong link.
How it works:
You find the usual setup: four cells forming a rectangle that all include the same two candidates (say 3 and 7).
One of those cells has an extra candidate, like 9.
Somewhere else in the same row, column, or box, there’s another 9 — and those two 9s form a strong link (meaning exactly one of them has to be 9).
Now here’s the key idea:
If the corner cell took 3 or 7 instead of 9, the rectangle would become deadly (two possible solutions). So the only way to avoid that is for this corner cell’s 9 to actually be true.
That lets you place the 9, and not just eliminate something, but make a definite placement.
5️⃣ Unique Rectangle Type 5
A Unique Rectangle Type 5 happens when a potential deadly rectangle interacts with a strong link between two different candidates inside that rectangle, not just a single “extra” number like in Type 4.
This means that within the rectangle, two of the corners each have extra candidates, and those extras are strongly linked to each other somewhere else in the puzzle.
You use that link to force a logical conclusion, either an elimination or a placement, that prevents the deadly rectangle from forming.
How it works:
You find a potential deadly rectangle, four cells that all include the same two candidates (say 3 and 7).
Two of those cells (on the same diagonal) each have one or more extra candidates, like 9 or 5.
Those extra candidates (9 and 5) are connected by a strong link, meaning one of them must be true.
Now, if both those extra candidates were false, you’d end up with a deadly rectangle (two solutions). So logically, one of them must be true, which lets you:
Eliminate one or both of the deadly rectangle’s base candidates (3 or 7) from certain cells, or
Sometimes even force one of the strong-linked candidates to be true.
In short:
Type 5 = the “chain reaction” rectangle. It’s like the Sudoku equivalent of a tripwire, if both extras failed, the puzzle would collapse into two solutions, so one must trigger, and you can use that to your advantage.
6️⃣ Unique Rectangle Type 6
A Unique Rectangle Type 6 occurs when a potential deadly rectangle connects to two different strong links, one for each of the rectangle’s two base candidates.
In other words:
You’ve got your classic rectangle (four cells, same two candidates, say, 3 and 7).
Somewhere else in the puzzle, there’s a strong link on 3s, and another strong link on 7s.
Those links connect (directly or indirectly) to cells inside the rectangle.
That double linkage creates a logical trap:
If both the “extra” candidates in the rectangle were false, the strong links would break and/or the puzzle would end up with two solutions (impossible).
So, by tracing those links, you can either force one value to be true or eliminate one or both base candidates from specific cells.
How it works:
You find a possible unique rectangle with candidates 3 and 7.
You identify a strong link on 3 (somewhere in the grid, only two 3s exist in a house).
You also identify a strong link on 7 (same idea).
Each strong link interacts with one of the rectangle cells, meaning changes to one affect the other.
Now, because both 3 and 7 are “locked” in separate strong links, both can’t disappear at once without breaking Sudoku’s one-solution rule.
That gives you logical eliminations, or sometimes even a forced placement, depending on how the links overlap.