Between Lines Sudoku: rules and tips

In between lines sudoku, each line has a circle at each end. Every digit on the line, not counting the circles, must lie strictly between the two circled digits.

One circle is the floor and the other the ceiling, and you don’t know which is which until the grid tells you. Measuring the gap between them is the key skill.

The rules

• Normal sudoku rules apply: 1 to 9 once in every row, column and 3×3 box.
• Along each line with circles at both ends, every digit between the circles is greater than one circled digit and less than the other.
• Lines can bend and step diagonally. Here they are three to six cells long, including the circles.

How to start

Ends and middles

An interior digit can never be 1 or 9, because it needs something smaller and something larger. The two circles can’t be equal or consecutive, since there must be room for at least one digit between them.

Measure the gap

If several interior cells share a house, they are all different, so the circles must be far enough apart to fit them all.

If the far circle were 1, the middle could be any four of 2 to 6; if 2, the middle is exactly 3, 4, 5 and 6.

Which end is low?

As soon as one interior digit is known, both circles are pinned to opposite sides of it. A 6 on the line means one circle is at most 5 and the other at least 7.

Common mistakes

• Letting an interior digit equal one of the circles. “Between” is strict.
• Assuming the interior digits must increase along the line. They can be in any order.
• Forgetting that interior digits in different houses may repeat.

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 lines, around eight at Lemma and about four at Conjecture, so each gap has to be read more carefully.

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

• Thermo SudokuDigits strictly increase from bulb to tip. Count the cells, bound the ends.
• Renban SudokuPurple lines hold runs of consecutive digits, in any order.
• Arrow SudokuThe circled digit equals the sum along its arrow. Bound circles and arrows.
• 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.