Empty Rectangle

In this situation, we have,

A Weak Link on the '4' candidate in cells 'A' and 'B'.
A Strong Link on the '4' candidate in cells 'B' and 'C'.

If cell 'A' has the value '4',

⇒ We would remove the '4' candidate from cells 'D' and 'E'.

⇒ Cell 'B' can't be a '4'

⇒ Cell 'C' must be '4'

⇒ Cell 'F' (and cell 'E') can't be a '4'.

This leaves no remaining possible position for the '4' value in the top-left region, i.e. we have reached an invalid state.

This means that cell 'A' can't have the value '4', and we can remove this candidate.

This is another example where we can apply the Empty Rectangle technique.

If cell 'A' takes the value '2',

⇒ Cell 'B' can't take the value '2'.

⇒ Cell 'C' can't take the value '2'.

⇒ Cell 'D' must take the value '2'.

⇒ Cell 'E' can't take the value '2'.

This leaves the center region with no remaining candidates, i.e. an invalid state

We can remove the '2' candidate from cell 'A'.

This is another example where we can apply the Empty Rectangle technique.

When looking for Empty Rectangles, the easiest place to start is to look at the Strong Links within the rows and columns of the puzzle - a puzzle will always have a lot more Weak links than Strong links.

You will then need to methodically check each of the Weak Links for each of the candidates, to see if the Empty Rectangle technique can be applied.

As with most techniques, it becomes easier to spot them with practice.

Can you find the Empty Rectangle here?

Did you find it?

Can you find the Empty Rectangle here?

Did you find it?

Can you find the Empty Rectangle here?

Did you find it?

This situation is 2 Strong Links - the technique works just as well, and you can apply the chain of reasoning in either direction.

That's everything you need to know for the Empty Rectangle technique!

Sudoku Academy

Empty Rectangle

Empty Rectangle