## 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 [click for larger image].

## 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 [click for larger image].

## Unique candidate 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 [click for larger image].

## 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 [click for larger image].