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Empty Rectangles

Points. An empty rectangle is single digit method with two truths that form a short single digit chain to eliminate a candidate that sees both ends. One end of the chain is a box set with more than 2 candidates. The technique gets its name from examples where the center of the box is empty, but this is not required. Examples with a center candidate in the box work exactly the same. 

 

 

Empty Rectangle Example 1. The first example is a theoretical drawing of an ideal empty rectangle. The red candidate in r8c2 can see both ends of the logic, in other words, it is covered by two of the covering links.

 

In terms of implications:

 

r2c2=5 => r8c2<>5

r2c2<>5 => 5r2c8 => r79c8<>5 => 5r8c79 => r8c2<>5 

 

In terms of truths and covers, 2 truths + 3 covers imply any candidate covered by two links can be eliminated. Thus r8c2<>5. 

 

 

 

 

Empty Rectangle Example 2. Examples 2 is almost exactly the same as the logic in example one, excprt the empty triangle box has three candidates.

 

Empty Rectangle Example 3. This example works in the same way, except that it combines a column truth with a box truth. Note, the red candidate is covered by the links in column 2 and row 8. The graphic option to show links to eliminatees is turned off.

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Empty Rectangle Example 4. The last example is that of an empty rectangle that is not empty. However, the logic is exactly the same as in the previous examples.