Palindrome Sudoku: rules, tips and free puzzles

In palindrome sudoku, each grey line reads the same from either end, like “level” or 12321. The first and last cells match, the second and second-to-last match, and so on.

That turns pairs of distant cells into twins, and anything you learn about one twin is instantly true of the other.

The rules

• Normal sudoku rules apply: 1 to 9 once in every row, column and 3×3 box.
• Each grey line reads the same from either end: cells the same distance from the two ends hold the same digit.
• Lines can bend and step diagonally. Here every line has an odd number of cells (five or seven), so each has a free middle cell.

How to start

Pair up the twins

Twins hold the same digit, so they can never share a row, column or box. Treat them as one cell that belongs to two sets of houses: a candidate removed from either twin is removed from both.

Twins see twice as much

Because each twin has its own row, column and box, the pair together sees up to six houses. Collect all the digits those houses contain and the twins’ candidates shrink fast.

The middle cell is free

On an odd-length line the middle cell has no twin, so the palindrome rule says nothing about it. Don’t over-constrain it.

Common mistakes

• Thinking the middle cell must match something.
• Assuming palindrome digits increase or follow a pattern. Only the mirror matters.
• Forgetting to copy eliminations across to the twin.

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 palindromes, around seven 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

• Renban SudokuPurple lines hold runs of consecutive digits, in any order.
• Between LinesEvery digit on a line sits strictly between its two circled ends.
• German WhispersNeighbours on a green line differ by at least 5. Fives are impossible there.
• 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.