Between Line Sudoku Help
Digits on between line must be between circled edges. In this case (image above) values can be 2, 3, or 4.
Circled cells are called edge cells, cells between the edges must have digits between edge digits.
In this case (image above) since one edge is 3 and there are two cells in between, between cells could be at least (4, 5) or (2, 1). But 2, 1 is not an option since other edge cell (circled cell) cannot be 0. This means edge cells with digit 3 must be lower. Minimal digits we can set on between line are (6, 7), since 4 and 5 aren't available. This means other edge cell can be 8 or 9.
If only one edge digit is set, in some cases we can conclude which edge is lower digit and which is higher digit.
Between cells can never have 1 or 9, because we cannot put 0 or 10 on edge cells.
When no edge digit is set, on longer between lines we can still remove some digits.
On between line with 4 between cells (6 with edge cells), where all cells are in the same house (box, column, row), edge cells cannot contain 5, because other edge cell would have to be 0 or 10.
On between line with 5 between cells (7 width edge cells) in the same house, edge cells for the same reason cannot contain 4, 5, or 6.
On between line with 6 between cells (8 width edge cells) in the same house, edge cells cannot contain 3, 4, 5, 6, or 7. In other words on this kind of between line, edge cells can be only 1, 2, 8 or 9.
On between line with 7 between cells (9 width edge cells) in the same house, edge cells cannot contain 2, 3, 4, 5, 6, 7 or 8. In other words on this kind of between line, edge cells can only be 1, or 9.
When between line is located in multiple houses (box, row, column) we take into account cells that are in the same house. On image below we have 4 between cells in row 1, and 5 between cells in box 2. So this between line must have 5 unique between cells. This tells us that edge cells can be 1,2,3 and 7,8,9 and between cells can contain 23456 or 34567 or 45678. In all cases between cells must contain 45.
