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On HuDoKu's page on Uniqueness, under Unique Rectangle, it says

A common mistake when looking for URs is to violate the "2 blocks" rule (see the Sudopedia article for an example).

Unfortunately, the Sudopedia link they give is broken.

I understand the "2 blocks rule" from the section above that note as meaning that the rectangle must be in exactly two blocks, but what mistake was the example supposed to show, and how can it cause a problem if I make that mistake?

ClickRick
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2 Answers2

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Could this be an alternative link? Unique Rectangles

The link is saying that if you end up with the 2 blocks like this (the four pink boxes can only have either 1 or 2 in them, "MadOverlord" named this Unique Rectangle pattern the Deadly Pattern apparently!):

enter image description here

then either:

  1. the setter has not created a sudoku with a unique solution (since there are two possible ways to populate the boxes)
  2. or you have gone wrong somewhere.

The writer from Sudoku Wiki goes on to say that if you know that there is a unique solution then you can use potential blocks like this to your advantage when solving the puzzle.

For example, in the below:

Potential Deadly Pattern

You will be able to see that you cannot place a 7 in any of the blue boxes as this will leave behind the deadly pattern, and so the 7 must be in the bottom left of that rectangle.

There are a few variations on this example on that page - You can draw conclusions about the numbers in more than just the four rectangle boxes themselves.

Personally, I am a bit wary of using this method as making any assumption in a sudoku makes me feel a little uneasy! It was an interesting read though.

To answer you question, I don't think that finding that you have "the deadly pattern" is the mistake, but it shows you that maybe somewhere earlier in the solving, you've made a mistake. Or else, there are multiple solutions. As we can see from this question, not many people like multiple solutions:

Why must a sudoku have a unique solution

I hope that helps? Or at least that the sudokuwiki link helps!

Community
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Ali
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    If you'd summarise that link here (partly so people don't have to click to read it, and partly in case that link breaks in the future) then I'll upvote and accept, because it tells me exactly what I wanted to know! – ClickRick Jun 30 '14 at 22:29
  • @ClickRick OK, I've done that now, I hope it is now a more useful answer to someone in the future. Thanks. – Ali Jul 01 '14 at 17:47
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Unique rectangles basically says that if you can find a group of four cells that form a rectangle, and such that two of them are in the same 9-block (which implies the other two also will be in the same block) and each have the same pair of numbers that can occur in them, then there can be two possible solutions that fit the Sudoku

For example if 2 and 7 are the numbers that can occur in the cells of the rectangle, then filling the Sudoku with

    2---7        7---2
1.  |   |  or 2. |   |
    7---2        2---7

will not make any difference as long as one pair of cells are in one 9-block and the other pair in another 9-block ( That is they are in two 9-blocks)

If each of the cell of the rectangle is in a different 9-block (That is 4 9-blocks in total), then this rule wont apply because interchanging a pattern 1 into pattern 2 would not result in a valid solution.

Where as if pairs of cells are in the same 9-block, then it would still make a valid solution

So, applying the unique rectangle rule only makes sense when the four grid cells are spread over two 9-blocks , or simply two blocks. I think this is what the article might have meant by "2 blocks" rule.

glugglug
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