All Sudoku Variants
9×9 · Constraint

Entropic Lines Sudoku

Also known as Entropy Lines Sudoku

Any three consecutive cells on an entropic line must include one low (1–3), one middle (4–6) and one high (7–9) digit.

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An example Entropic Lines puzzle: every three cells in a row on the line hold one low (1–3), one middle (4–6) and one high (7–9) digit — here 1, 5, 9, 3, 7.

Entropic Lines Sudoku splits the digits into three "entropy" groups — low (1, 2, 3), middle (4, 5, 6) and high (7, 8, 9) — and draws lines with one rule: any three cells in a row along the line must come from three different groups. One low, one middle, one high, always, no matter where you look on the line.

The rule: one from each group, every three cells

Slide a window of three cells anywhere along the line: it must contain exactly one low, one middle and one high digit. Below, the colours mark the groups — every run of three (2-5-8, then 5-8-1, then 8-1-4) has one of each.

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Low 1–3, middle 4–6, high 7–9: every three-in-a-row has one of each.

A worked example, step by step

Take a line whose first two cells are a 2 and a 5, with the third still empty.

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Step 0. First two cells: 2 (low) and 5 (middle).

Step 1 — name the groups. The 2 is a low digit and the 5 is a middle digit. The first three cells must have one from each group, so the two groups already used are low and middle.

Step 2 — the third must be high. The only group left is high, so the third cell must be a 7, 8 or 9 — before any other clue touches it.

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Step 2. Low and middle are taken, so the third cell is high: 7, 8 or 9.

The pattern repeats

Because every three-cell window needs all three groups, the groups march in a fixed cycle along the whole line — low, middle, high, low, middle, high, and so on (in whatever order the line starts). So once you know the group of any two adjacent cells, the group of every other cell on the line follows. A long entropic line is one of the most constraining features you can meet.

Solving strategy

  • Think in groups first, digits second. Fix the low/middle/high pattern along the line before worrying about exact values.
  • Two cells set the cycle. Any two neighbours pin the group of every cell on the line.
  • Combine with the grid. Once a cell is limited to one group of three digits, the rows, columns and boxes usually finish the job.
  • Feed the grid. Each digit fixed on the line behaves like a given for its row, column and box.

Common mistakes

  • Only checking the first three. Every consecutive three must have one of each group, not just the opening trio.
  • Mixing up the groups. Low is 1–3, middle 4–6, high 7–9 — a 6 is middle, not high.
  • Reading a group as a fixed digit. "High" means 7, 8 or 9 — the exact value still needs the ordinary rules.
  • Forgetting ordinary Sudoku. Line cells still can't repeat within a row, column or box.

Can I play it here?

Not yet — Entropic 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: