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Empty Rectangle

Expert· L8
Elimination

An Empty Rectangle looks at one digit inside a box. The candidates avoid one row–column corner of the box, leaving an “L” or rectangle shape of possible cells — with an empty corner.

Paired with a strong link outside the box, both stories sting the same victim — same family as turbot / short AIC endings.

Why it works

Inside the box, if the digit is not in one row of the box, it must be in the other row of the pattern (and similarly for columns). Paired with a strong link outside, one of two stories is always true — and both stories attack the same victim cell.

So that victim cannot be the digit. You are again using “both cases sting the same place.”

Demonstration

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In a box, draw where one digit can still go. Look for an empty-rectangle shape — candidates on two lines that leave a corner empty.

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Combine that shape with a strong link on 4 outside the box. That is an Empty Rectangle.

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Whatever branch is true inside the box, together with the strong link, 4 is forced somewhere that hits the same target.

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Eliminate 4 from the marked target cell(s) (red). Both worlds sting them.

Example 1

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Find an empty-rectangle shape in a box plus a conjugate link.

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This Empty Rectangle is on 4.

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Remove 4 from the target (red). Both cases attack it.

Example 2

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Find an empty-rectangle shape in a box plus a conjugate link.

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This Empty Rectangle is on 7.

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Remove 7 from the target (red). Both cases attack it.

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