Chute Remote Pairs

Chute Remote Pairs is a short, sharp pattern that uses the geometry of a band or stack to break the tie between two identical bivalue cells. It needs no chains and no colouring — just two matching cells and a quick look at one box.

What the pattern is

A chute is three boxes in a line: a horizontal band of three boxes or a vertical stack of three. There are six chutes in a 9x9 grid.

Inside one chute, find two cells that both hold exactly the same two candidates, say {3,6}, and that do not see each other. Because they are in the same chute and cannot share a row, they sit in different boxes and different lines. That leaves one box of the chute with neither cell in it, and one line of the chute with neither cell on it.

The three spare cells are where that unused line crosses that unused box. They decide the pattern.

If both pair cells took the same digit, that digit would already be used in two boxes of the chute on two different lines. The third box would then be forced to place the digit on the remaining line — inside the spare cells. So if the spare cells cannot hold the digit, the two pair cells cannot both hold it either.

When to look for it

• When you already spotted two identical bivalue cells and they are not a naked pair, so nothing obvious follows.
• When both of them fall inside the same band or the same stack.
• When the third box of that chute is fairly full, which is what makes a digit go missing from the spare cells.

Check both digits of the pair. If both are absent from the spare cells, you get two eliminations at once.

How to apply it, step by step

1. Find two cells with the same two candidates inside one band or one stack, in different boxes, on different lines.
2. Identify the box of that chute containing neither cell.
3. Identify the line of that chute containing neither cell.
4. The three spare cells are the intersection of that box and that line.
5. Take a digit of the pair that is absent from all three spare cells. Neither of the two pair cells can share that digit with the other, so the other digit is forced into one of them.
6. Remove that other digit from every cell that sees both pair cells.

A worked example

Band of rows 1 to 3. Only the digits that matter are shown:

          box 1        |     box 2     |      box 3
  r1     . {3,6} .     |  .   .   .    |   .   .   .
  r2     .   .   .     |  . {3,6} .    |   .   .   .
  r3     .   .   .     |  .   .   .    |  no 6, no 6, no 6   <- spare cells

The pair cells are r1c2 in box 1 and r2c5 in box 2, both {3,6}. They share no row, no column and no box, so they do not see each other. The unused box is box 3, the unused row is row 3, and the spare cells are r3c7, r3c8, r3c9.

Those three cells have no 6 left. Now suppose both pair cells were 6. Box 1 would use its 6 in row 1, box 2 would use its 6 in row 2, so box 3 would have to place its 6 in row 3 — in the spare cells. Impossible. So the two pair cells are never both 6.

Therefore no cell that sees both of them can be a 3: a 3 there would push both pair cells to 6. Erase the 3 from r2c1, r2c2, r2c3 (they see r1c2 through box 1 and r2c5 through row 2) and from r1c4, r1c5, r1c6 (box 2 and row 1).

Common mistakes

• Using a naked pair. If the two cells see each other, this is an ordinary naked pair and the chute logic adds nothing.
• Checking the whole third box. Only the three spare cells on the unused line matter. The other six cells of that box are irrelevant.
• Eliminating the missing digit. The absent digit supplies the contradiction; the digit you actually delete is its partner.
• Forgetting stacks. Vertical chutes work identically, with columns in place of rows. Half the available patterns live there.

Where you meet it

Chute Remote Pairs sits early in the tough tier, right beside the fish patterns. It shows up on hard classic Sudoku, usually as a quick alternative when a fish scan comes back empty and you want one more cheap deduction before starting on chains.