daj95376 wrote:Then I'd know if any of the following
four Unique Rectangles can be reduced.
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*-----------------------------------------------------------*
| 6 1 8 | 5 *34 *34 | 9 7 2 |
| 3 9 7 | 1 8 2 | 5 4 6 |
| 2 5 4 | 7 69 69 |*13 8 *13 |
|-------------------+-------------------+-------------------|
| 4 *68 9 | 3 567 568 | 2 1 57 |
| 7 *68 1 |*69 2 5689 | 36 3569 4 |
| 5 2 3 | 4 679 1 | 8 69 79 |
|-------------------+-------------------+-------------------|
| 8 4 5 |*69 13 369 | 7 2 139 |
| 9 7 2 | 8 134 345 | 136 356 135 |
| 1 3 6 | 2 59 7 | 4 59 8 |
*-----------------------------------------------------------*
This is a good opportunity to make a point about the way candidate grids are often presented -- namely, among the singletons no attempt is made to distinguish the
given digits (clues) from the
solved digits. This distinction is important when the solving-methods of interest include unique-solution strategies!
E.g, in addition to the UR's already indicated in the above grid, there are many potential unavoidable rectangles from which inferences may be drawn
if their "corner singletons" are solved digits and not clues; here are four potential unavoidable rectangles indicated by four different bracket-types:
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*-----------------------------------------------------------*
| 6 1 8 | 5 34 34 | 9 7 2 |
| 3 9 7 | 1 8 2 |(5) (4) 6 |
| 2 5 4 | 7 69 69 | 13 8 13 |
|-------------------+-------------------+-------------------|
|{4} <8>6 9 | 3 567 568 |<2> 1 {7}5 |
|{7} 68 1 | 69 2 5689 | 36 3569 {4} |
| 5 <2> 3 | 4 679 1 |<8> 69 79 |
|-------------------+-------------------+-------------------|
|[8] 4 5 |[9]6 13 369 | 7 2 139 |
|[9] 7 2 |[8] 134 345 | 136 356 135 |
| 1 3 6 | 2 59 7 |(4) (5)9 8 |
*-----------------------------------------------------------*
Of these four, it can be concluded (assuming a unique solution) that in the original puzzle at least one of the singletons in the <8>6-<2>-<8>-<2> rectangle was given as a clue, and so was at least one of the singletons in the {4}-{7}-{4}-{7}5 rectangle. Consequently, no unique-solution strategy can be based on these two potential unavoidable rectangles.
OTOH, one can't tell (from the information as-presented) whether some of the singletons in the other two rectangles were given as clues; if none were clues, then [8]-[9]-[8]-[9]6 places that 6, and (5)-(4)-(5)9-(4) places that 9.
