All Sudoku Variants
9×9 · Constraint

Descriptive Pairs Sudoku

A pair of digits X and Y outside a row or column means the Xth cell holds Y, or the Yth cell holds X — at least one of the two must be true.

5 7 1 4 5 9 2 81 54 71 3

An example Descriptive Pairs puzzle. Beside row 1 the pair {1, 5} holds because the 1st cell is 5 — the 5th cell being a 1 would satisfy it too.

Descriptive Pairs Sudoku writes a pair of digits outside some rows and columns. The pair describes a position relationship, and it is deliberately ambiguous: for the clue {X, Y}, either the Xth cell holds Y, or the Yth cell holds X — and possibly both. You never learn which from the clue alone; the rest of the grid settles it. It is a cousin of Numbered Rooms, loosened into an "at least one" rule.

The rule: at least one of the two holds

Take the clue "3 7" beside a row. Counting inward from that edge, either the 3rd cell contains a 7, or the 7th cell contains a 3 — at minimum one is true. Below, the 3rd cell resolves to 7 (the 7th cell could still be a 3 as well).

3 7 7

Clue {3, 7}: here the 3rd cell holds 7 (green). The other option — the 7th cell (blue) holding 3 — may also be true, but at least one must be.

How to read it

The clue is a disjunction. It rules out only the case where neither relationship holds. Early on that is weak, but it grows sharp as the grid fills: the moment you know the 3rd cell is not 7, the clue forces the 7th cell to be 3, and vice versa.

Equal-looking pairs are special. A clue like {2, 2} is really just "the 2nd cell is 2", since both halves say the same thing — an exact placement.

Solving strategy

  • Wait for one side to fail. As soon as one of the two positions is blocked, the other becomes a forced placement.
  • Use the digits as exclusions. Whichever way it resolves, both X and Y are constrained to specific early cells, keeping them out of others.
  • Prize the tight positions. Small numbers in the pair point at cells near the edge, where the near box also limits the options.
  • Feed the grid. Every digit a pair fixes behaves like a given for its row, column and box.

Common mistakes

  • Assuming both hold. Only at least one is guaranteed — do not place both until the grid proves it.
  • Fixing which side is true too early. The clue is symmetric; let other constraints break the tie.
  • Counting from the wrong end. Always count inward from the edge the clue is written on.
  • Dropping ordinary Sudoku. The placed digits must still obey their row, column and box.

Can I play it here?

Not yet — Descriptive Pairs 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: