9×9 · Irregular Region

Toroidal Sudoku

Also known as Torus Sudoku, Wraparound Sudoku

The grid wraps at its edges like a torus, so jigsaw regions can run off one side and continue on the other.

1 5 9 3 7

An example Toroidal Sudoku: the grid is a torus — the right edge wraps to the left and the top to the bottom, so a region can run off one side (arrows) and continue on the other.

Toroidal Sudoku treats the grid as a torus: the right edge wraps around to the left and the top to the bottom. Jigsaw regions can run off one side and continue on the other, so a single region may span the grid's edges as if they were joined.

The rule: the grid wraps around

Rows, columns and regions all still need 1–9, but regions may wrap across the borders. Below, one region (purple) exits the right edge and re-enters on the left — the two shaded strips are the same wrapping region.

A region wrapping the edges: the cells on the right and left belong to one region across the torus.

Solving strategy

  • Follow regions across the edges. A region leaving one side continues on the opposite side.
  • Scan wrapping units as one. Treat the two edge strips of a wrapping region as a single region for 1–9.
  • Mind the wrap on lines too. Some variants wrap the row/column logic as well — check the puzzle.
  • Feed the grid. Each digit placed behaves like a given for its row, column and (wrapping) region.

Common mistakes

  • Treating the edges as walls. On a torus the borders join — regions and (sometimes) lines continue across.
  • Splitting a wrapping region. The edge strips are one region and share the 1–9 requirement.
  • Ignoring the ordinary rules. Rows, columns and regions still need 1–9.

Can I play it here?

Not yet — Toroidal 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: