Renban Sudoku: rules, tips and free puzzles

In renban sudoku, purple lines hold sets of consecutive digits, in any order. A three-cell renban might be 4, 6, 5 or 9, 7, 8, but never 3, 5, 6.

The name comes from the Japanese for “consecutive numbers”. Renban lines are fun because their length alone tells you so much.

The rules

• Normal sudoku rules apply: 1 to 9 once in every row, column and 3×3 box.
• Each purple line contains a set of consecutive digits, in any order, with no repeats.
• Lines can bend, step diagonally and cross box borders. Here they are three to six cells long.

How to start

Length is information

A renban of L cells holds one of 10 − L possible runs. Long lines must contain the middle digits: a five-cell line always includes 5, and a six-cell line always includes 4, 5 and 6.

Watch the extremes

If a line contains a 1, nothing on it is bigger than its length. If it contains a 9, nothing is smaller than 10 − L. A digit that is ruled out of a line often decides which end of the number line the run lives at.

Gaps break runs

If a three-cell line can’t contain 5, it must be entirely below 5 (from 1–4) or entirely above (6–9). Splitting a line into “low run” or “high run” is often the first real deduction.

Common mistakes

• Assuming the digits appear in order along the line. Any order is fine.
• Allowing a repeat because a line crosses into a different box. Renban digits never repeat.
• Forgetting that the run must be unbroken: 3, 4, 6 is not a renban.

How the ranks scale difficulty

Every puzzle type on Hoot’s Puzzles comes in four ranks, named after the stages of a mathematical idea. Lemma is the warm-up: about a dozen more digits are given than logic strictly needs, and singles plus the variant’s own rule will carry you through. Proposition needs a real idea or two, typically pointing and claiming. Theorem is near-minimal, so almost every clue is load-bearing and you may need pairs. Conjecture gives the fewest digits and sparser rule clues: expect to think hard.

Higher ranks use fewer renban lines, around eight at Lemma and about four at Conjecture.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• German WhispersNeighbours on a green line differ by at least 5. Fives are impossible there.
• Between LinesEvery digit on a line sits strictly between its two circled ends.
• Thermo SudokuDigits strictly increase from bulb to tip. Count the cells, bound the ends.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.