All Sudoku Variants
9×9 · Constraint

Palindrome Sudoku

Grey lines are palindromes: the digits read the same forwards and backwards along each line.

1 837573

An example Palindrome puzzle: cells equidistant from the centre hold equal digits — 3, 7, 5, 7, 3.

Palindrome Sudoku draws grey lines across the grid that read the same forwards and backwards. Along each line, cells the same distance from the two ends hold equal digits — just as a palindrome word like "level" mirrors around its middle. The line itself places no digits, but its mirror symmetry links cells all over the grid.

The rule: mirror around the centre

Fold a palindrome line at its midpoint and the two halves must match: the first cell equals the last, the second equals the second-to-last, and so on. A five-cell line therefore has the pattern a-b-c-b-a. Below, the line reads 3-7-1-7-3 — a genuine palindrome.

37173

A palindrome line reads the same both ways: 3-7-1-7-3. Mirror cells hold equal digits.

Reading the mirror pairs

The power of a palindrome is that it forces distant cells to be equal — the opposite of Sudoku's usual "all different" instinct. Each coloured pair below must hold the same digit. That has an immediate consequence: if two mirror cells ever fall inside the same row, column or box, the line is impossible, because equal digits cannot share a unit. So a palindrome's length and route are tightly limited by where its mirror cells land.

On a six-cell line the mirror pairs (matching colours) must be equal — and so can never share a row, column or box.

How it helps you solve

Every value you place on a palindrome is instantly copied to its mirror, so one deduction does double duty. Better still, the mirror constraint chains: if cell a equals cell e, and cell e is pinned by its row, then cell a is pinned too, perhaps far across the grid. Look for mirror cells that sit in already-crowded units — they often resolve at once and then hand you their partner for free.

Solving strategy

  • Copy across the mirror. Any digit placed on the line appears immediately at its mirror position.
  • Check for illegal pairs. Mirror cells in the same unit are impossible — use that to rule candidates out.
  • Exploit crowded partners. When one mirror cell is heavily constrained, solve it and copy to the other end.
  • Feed the grid. Each mirrored placement behaves like two givens for their rows, columns and boxes.

Common mistakes

  • Making mirror cells different. The pairs must be equal, not distinct — this is the reverse of the usual Sudoku rule.
  • Forgetting the centre. An odd-length line has a lone middle cell that mirrors itself and is otherwise free.
  • Allowing a pair in one unit. Equal mirror cells can never sit in the same row, column or box.
  • Ignoring the ordinary rules. The palindrome is an extra layer over the usual row, column and box constraints.

Can I play it here?

Not yet — Palindrome 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: