127.0.0.1 at 11:30, 29 October 2021

2021-10-29T11:30:57Z

← Older revision		Revision as of 11:30, 29 October 2021
Line 30:		Line 30:
	The result is this [[Nice Loop]] fragment:		The result is this [[Nice Loop]] fragment:
	[r1c5]=8\|9=[r3c2]		[r1c5]=8\|9=[r3c2]

			== External Links ==

			* [http://forum.enjoysudoku.com/almost-unique-rectangles-description-and-use-in-nice-loops-t2751.html almost-unique-rectangles-description-and-use-in-nice-loops] on the new Sudoku Player's forum.

			[[Category:Uniqueness]]

127.0.0.1: Created page with "An '''Almost Unique Rectangle''' or '''AUR''' is a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four..."

2021-10-29T11:27:16Z

Created page with "An '''Almost Unique Rectangle''' or '''AUR''' is a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four..."

New page

An '''Almost Unique Rectangle''' or '''AUR''' is a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four cells allow a [[Uniqueness Test]].

=== Example 1 ===

[[Image:aur-1.png]]

As one can see, the 4 cells in r13c25 would form a [[deadly pattern]] for digits 1 and 2 if it were not for the extra candidates for [[digit]] 8 and 9.

If the candidates for digit 8 were not present, it would form a '''Uniqueness Test 2''', allowing us to eliminate all other candidates for digit 8 in row 1.

If the candidates for digit 9 were not present, it would form a '''Uniqueness Test 2''', allowing us to eliminate all other candidates for digit 9 in row 3.

In its present form, we can make no direct eliminations, but can use this pattern in a nice loop, using the strong link between digit 8 in r1c25 and digit 9 in r3c25.

The result is this [[Nice Loop]] fragment:
[r1c2|r1c5]=8|9=[r3c2|r3c5]

=== Example 2 ===

To show that this also works with 1 extra candidate at both sides:

[[Image:aur-2.png]]

If the candidate for digit 8 were not present, it would form a '''Uniqueness Test 1''', allowing us to eliminate all candidates for digit 9 for all [[peer]]s of '''r3c2'''.

If the candidate for digit 9 were not present, it would form a '''Uniqueness Test 1''', allowing us to eliminate all candidates for digit 8 for all peers of '''r1c5'''.

In its present form, we can make no direct eliminations, but can use this pattern in a nice loop, using the strong link between digit 8 in r1c5 and digit 9 in r3c2.

The result is this [[Nice Loop]] fragment:
[r1c5]=8|9=[r3c2]

Almost Unique Rectangles - Revision history

127.0.0.1 at 11:30, 29 October 2021

127.0.0.1: Created page with "An '''Almost Unique Rectangle''' or '''AUR''' is a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four..."