Chute Remote Pairs in Sudoku

Specialist S3 Chains

Chute Remote Pairs uses two cells with the same candidate pair in one band of three boxes or one stack of three boxes. A third group of cells, the bridge, rules out both endpoints holding one digit. At least one endpoint must hold the other, so cells seeing both lose that other digit.

A candidate is a digit that can still go in an empty cell. Cells see each other when they share a row, column or 3×3 box. A strong link means a digit has exactly two possible cells in one such group: exactly one must contain it.

How to spot it

  • Choose three boxes side by side or three stacked vertically. This is a chute.
  • Find two cells in it containing only the same two candidates. They must be in different boxes and different rows for a horizontal chute, or different columns for a vertical chute.
  • Find the unused box and unused row or column. The three cells where they meet are the bridge.
  • Check whether one pair digit is absent from all three bridge cells, both as a candidate and as an already placed digit. A placed digit counts as present.

Why it works

For example, let both endpoints have 7/9, with no 7 in the bridge. If both endpoints were 7, the third row of a horizontal chute would need its 7 in the unused box: exactly where the bridge is. That is impossible.

So the endpoints cannot both be 7. At least one must be 9, and any other cell seeing both endpoints loses 9. The same proof works with columns in a vertical chute.

If both pair digits are absent from the bridge, apply that argument to each digit. The endpoints must take different digits, so cells seeing both lose both candidates.

In that two-digit case, Sudokuno also removes both candidates from the other cells in each endpoint's row within its box, or its column within its box in a vertical chute.

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 a candidate to cross it out; click it again to restore it. Remove the 2 candidates ruled out by this technique, then press Check. This exercise leaves your game unchanged.

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 The two endpoints are highlighted. They hold the same pair, lie in one chute and do not see each other.
  2. Hint 2 The bridge cells are added. Check which pair digits are absent, counting both candidates and placed digits.
  3. Hint 3 The targets are marked. For each pair digit absent from the bridge, the endpoints cannot both hold it, so cells seeing both lose the other digit. If both are absent, the hint also explains the extra removals within each endpoint's box.

For each digit blocked in the bridge, the other pair digit is removed from cells seeing both endpoints. Check the two digits separately; if both are blocked, both deductions apply.

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 covers two-endpoint Chute Remote Pairs in horizontal and vertical chutes, including the case where both pair digits are blocked in the bridge.

Where to go next

  • XYZ-Wing An XYZ-Wing has a pivot with three candidates and two wings with two each. The pivot sees both wings, whose pairs come from its three candidates. The digit shared by the wings must fill one of the three cells, so any other cell seeing all three loses it.
  • Y-Wing A Y-Wing uses three cells with two candidates each. One cell, the pivot, sees both wings. Whichever digit fills the pivot, one wing must hold the digit shared by the wings, so any cell seeing both wings loses that candidate.
  • W-Wing A W-Wing connects two cells holding the same candidate pair through a strong link on one digit. This proves that at least one of the pair cells holds the other digit. Remove that other digit from any cell seeing both pair cells.

All Sudoku techniques