3.1. Singles#
3.1.1. Basic Solving Without Pencil Marks#
- Many good sites that describe these techniques better than me rehashing the information here:
3.1.2. Exposed Singles#
Hodoku provides a good explanation of Exposed Singles.
3.1.4. Locked Singles#
3.1.4.1. Pointing Locked Candidates#
Hodoku provides a good explanation of Pointing Locked Candidates.
3.1.4.2. Claiming Locked Candidates#
Hodoku, provides a good explanation of Claiming Locked Candidates.
3.1.5. Empty Rectangles#
Empty Rectangles are a special case of Mutant X-Wings They can also be found by noticing 3 to 5 same value candidates in a box that describe both a row and a column.
Figure 3.1: Empty Rectangle Pattern#
In Figure 3.1: , the three X candidates in box 1 describe row 3 and column 2.
X can only be True once in Box 1, therefore:
If Xr1c2 is True then:
X cannot be True anywhere else along column 2, and
Xr3c13 cannot be True in the box either, X is True somewhere along row 3 outside box 1.
If an X is found along column 2, such as Xr7c2, and if it forms a strong link with another candidate X along row 7 outside of tower 1, such as Xr7c8; then because Xr7c2 cannot be True, Xr7c8 must be True, and if Xr7c8 is True, Xr3c8 cannot be True.
If Xr1c2 is False then:
Either Xr3c1 or Xr3c3 is True, ensuring that The Truth does not lie along row 3 outside box 1
Therefore, irrespective whether Xr1c2 is True or not, if Xr7c28 are strongly linked then Xr3c8 cannot be True and can be eliminated.
Similarly:
If Xr3c13 is a truth then:
X cannot be True anywhere else along row 3, and
Xr1c2 cannot be True in the box either, X is True somewhere along column 2 outside box 1.
Where an X is found along row 3, such as Xr3c8, and it forms a strong link with another candidate X along column 8 outside of floor 1, such as Xr7c8, then because Xr3c8 cannot be True, Xr7c8 must be True, and if Xr7c8 is True, Xr7c2 cannot be ‘The Truth’ along column 2.
If both Xr3c13 are False then:
Xr1c2 is True, ensuring that The Truth does not lie along column 2 outside box 1
Therefore, irrespective whether Xr3c13 is ‘A Truth’ or not, if Xr37c8 are strongly linked then Xr8c2 cannot be True and can be eliminated.
A box with two same value candidates can be resolved as an Empty Rectangle, however these patterns overlap with Turbot Fish and Grouped X Chains. Of these three patterns, a Turbot Fish is the easiest to resolve.