9×9 · Constraint

Between Lines Sudoku

Also known as Between Line Sudoku

A line strung between two circled cells may contain only digits that fall numerically between the two endpoint values.

5 32469

An example Between Lines puzzle: the two darker ends bound the line; every cell between them lies strictly between the end digits — here 4 and 6 between 2 and 9.

Between Lines Sudoku draws a line strung between two circled cells. The rule is a squeeze: every cell on the line must fall numerically between the two circled endpoint values. If the ends are 2 and 8, the line can only use the digits in between — 3, 4, 5, 6 or 7.

The rule: stay between the two ends

Read the two circled endpoints. Each cell on the line between them must be strictly larger than the smaller end and strictly smaller than the larger end. Below, the ends are 2 and 8, and the middle cells hold 4, 5, 6 — all between 2 and 8.

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Ends 2 and 8; the line cells (4, 5, 6) all lie between them.

A worked example, step by step

Take a line whose circled ends are already solved as 2 and 8.

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Step 0. The ends are 2 and 8; three line cells are empty.

Step 1 — read the range. The endpoints are 2 and 8, so every cell between them must be strictly greater than 2 and strictly less than 8 — that is, one of 3, 4, 5, 6 or 7. Both 1, 2, 8 and 9 are ruled out at once.

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Step 1. Every line cell is limited to {3, 4, 5, 6, 7}.

Step 2 — narrow with the grid. Those five candidates already exclude four digits per cell; the rows, columns and boxes crossing the line then trim them further, often to a single value. The wider the gap between the ends, the more room the line has — a gap of 1 or 2 leaves no legal digit at all, so such endpoints are impossible.

Solving strategy

  • Solve the ends first. Two known endpoints instantly fix the allowed band for the whole line.
  • Delete the outside band. Strike every digit at or beyond each endpoint from the line cells.
  • Mind the gap. Endpoints must be far enough apart to leave room — 2 and 4 allow only a 3.
  • Feed the grid. Each digit fixed on the line behaves like a given for its row, column and box.

Common mistakes

  • Including the endpoints. Line cells are strictly between the ends — never equal to either.
  • Impossible narrow gaps. Endpoints one apart (like 4 and 5) leave nothing between them, so that can't happen.
  • Forgetting which end is which. The band is between the smaller and larger value, whichever circle holds which.
  • Ignoring ordinary Sudoku. Line cells still can't repeat within a row, column or box.

Can I play it here?

Not yet — Between Lines Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: