Impossible combination IC
If none of a cell's candidates match with one of the strip's
combinations and those digits do not occur in any of the strip's other
combinations, those candidates can be removed from all cells in the
strip.
In the example, the sum 11 in 2 cells has combinations
[2,9],[3,8],[4,7],[5,6]. The left cell does not contain either 5 or
6, but both are candidates in the right cell. Neither of these symbols
occurs in any of the other combinations. For 5 to be the solution for
the right cell it would need a 6 in the left cell, but the 6 has
already been removed. Likewise for 6 to be the solution for the right
cell it would need a 5 in the left cell. Hence, both can be removed
from the right cell.
Unique intersections UI
If the combinations for intersecting rows and columns have in common
exactly one
unique digit, that digit must occur in the intersecting cell, and
so all other candidates can be deleted from that cell.
The sum down, 16, has one combination [7,9] and the sum across, 17, has one
combination [8,9]. At the intersection of this row and column only 9
is possible so all the other candidates (a 7) can be deleted.
Unique candidate's combination impossible UC
A strip has a combination with a unique digit. If this unique digit
remains as a candidate in one cell while a second cell in the strip does
not contain any of the other digits for its combination, the unique
digit can be removed from the first cell.
In the example the sum 7 in 2 cells has three combinations
[1,6],[2,5],[3,4] and so digits 1,2,3,4,5,6, are unique.
The program has discovered that the left cell in the
row does not contain 6. For 1 to be the solution in the other cell a 6
is required so the 1 can be deleted.
Hidden single H1
When a strip has a unique combination and one of the combination's
digits occurs in only a single cell, it must be the solution for that
cell and all the other candidates in the cell can be removed.
In the
example the sum 28 - 4 in 3 remaining cells has the unique combination
[7,8,9] and the bottom cell is the only one left with a candidate
7, so all other candidates (8,9) can be removed from that cell.
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