Chute Remote Pairs in Sudoku

Specialist S3 Chains

A chute is three boxes in a line - either three side by side or three stacked. If you find two cells in the same chute holding exactly the same candidate pair, and they share no row, column or box, then the three bridge cells in the unused line settle the matter. If one of the pair candidates is missing from the bridge, the other can be removed from the cells that see both ends.

How to spot it

  • Pick a chute: three boxes side by side, or three stacked on top of each other.
  • Find two cells in that chute with exactly the same two candidates.
  • The two endpoints must sit in different lines and different boxes within the chute - they must not be able to see each other.
  • That leaves one line and one box unused. The bridge is the three cells where they meet.
  • Check whether one of the pair candidates is completely absent from the bridge. A digit already placed in a bridge cell counts as absent too, not just a missing pencil mark.

Why it works

If one pair candidate is missing from all three bridge cells, the two endpoints cannot both be that digit. If they were, the chute's third line would need that digit in its third box - that is, in one of the bridge cells - and there is no room left for it.

Since the endpoints hold only those two candidates, and they cannot both be the blocked digit, at least one of them must be the other digit in the pair.

It is that other digit - the one still available in the bridge - that gets eliminated. Any cell seeing both endpoints cannot hold it, because one of the endpoints does.

If both pair candidates are missing from the bridge, the endpoints must take one each. Then the cells seeing both endpoints lose both digits, and so do the remaining cells in each endpoint's own part of its box.

A real example from Sudokuno

The board below is a real Sudokuno puzzle, shown exactly as it stands just before Chute Remote Pairs applies. Everything up to this point was solved with ordinary techniques.
9
4 8 5 1 6
6 4 8 7 1 5
9
1 6
9 4 7 8
6 1
9
4 9
6
8 1
1
7
4 6
2
6
1
9
4 8
1 6 5
1 2 4 5 6
9 3

Click away the candidates the technique removes - 2 of them - then press Check. Nothing is saved, and your own game is untouched.

Sudoku: SNC-00582 — Sudokuno

  • Candidate pair 3 and 5
  • Houses: row 5, column 3 and box 4
  • Endpoints: R5C3 and R6C8
  • Bridge cells: R4C4, R4C5 and R4C6
  • Removes 3 from R5C7 and R6C2
  • Step 18 of 52 in the solve

Key: endpoints bridge cells target cells

How the hint helps you

Sudokuno's hint reveals the structure in three steps, without giving away the digit straight away.

  1. Hint 1 Find the two cells holding the same candidate pair that sit in one chute without seeing each other. Sudokuno highlights the endpoints straight away.
  2. Hint 2 Look at the three highlighted bridge cells in the unused row. Which of the pair candidates can still go there?
  3. Hint 3 If a pair candidate is missing from the bridge, the endpoints cannot both be that digit - so the other pair candidate can be removed from the highlighted cells that see both ends.

This one is easy to remember backwards: the digit you remove is the one still available in the bridge, not the one that is missing. If the chute is vertical, the hint says the same thing with columns instead of rows.

Ready to try it yourself?

You will get a real Sudokuno puzzle at Specialist level S3, where Chute Remote Pairs is needed to finish it.

Practise Chute Remote Pairs

What Sudokuno covers

Sudokuno finds pairs with two endpoints. Longer remote-pair chains are not implemented. W-Wing builds on a related idea - two cells with the same pair - and has a page of its own.

Where to go next

  • XYZ-Wing An XYZ-Wing is a Y-Wing whose pivot has three candidates instead of two. The two wings have two candidates each, both drawn from the pivot's three, and they share exactly one candidate with each other. That shared candidate must occupy one of the three cells - the pivot included - so it can be removed from any cell seeing all three.
  • Y-Wing A Y-Wing is three cells that each have exactly two candidates. The pivot sees both wing cells. It shares one candidate with each wing, and the two wings have a third candidate in common. That third candidate has to land in one of the wings, so it can be removed from any cell that sees both of them.
  • W-Wing A W-Wing starts with two cells that have exactly two candidates each, and the same two: say 7 and 9. Somewhere else on the board, one of those digits - say 7 - has exactly two places left in a single row, column or box, and each of the two cells sees one of those two places. That is enough to prove that at least one of the two cells holds 9, so any cell that sees both of them cannot.

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