All Sudoku Variants
9×9 · Constraint

Anti-Diagonal Sudoku

Each of the two main diagonals may contain only three different digits.

1 2 3 1 2 3 1 2 3

An example Anti-Diagonal puzzle: the main diagonal carries only three different digits — 1, 2, 3 — each appearing three times.

Anti-Diagonal Sudoku puts a rule on the two main diagonals: each of them may contain only three different digits. Since a diagonal has nine cells, that means each of its three values appears exactly three times. It is the mirror image of X-Sudoku, which insists a diagonal hold all nine different digits — here you want as few as possible.

The rule: three values fill a diagonal

Look at a main diagonal: it holds nine cells but only three distinct digits, each three times. (They still can't break the ordinary rules — the three copies land in different rows, columns and boxes.) Below, the shaded main diagonal uses just 2, 5 and 8.

2 5 8 2 5 8 2 5 8

The main diagonal uses only three values — 2, 5 and 8 — each appearing three times.

A worked example, step by step

Suppose the top of a main diagonal already shows a 2, a 5 and an 8, and the rest of the diagonal is empty.

2 5 8

Step 0. The diagonal shows 2, 5, 8 so far; six cells remain.

Step 1 — three values are already used. The diagonal is allowed only three distinct digits, and 2, 5 and 8 have used up all three. So no fourth value can ever appear on it.

Step 2 — every remaining cell is 2, 5 or 8. Each of the six empty diagonal cells must be one of those three digits — a huge restriction that ordinary Sudoku, allowing all nine, could never impose.

2 5 8258258258258258258

Step 2. The rest of the diagonal is limited to {2, 5, 8}.

Why so few values is so strong

Capping a diagonal at three digits does two things at once. It forces those three digits to appear three times each — so they cannot be needed elsewhere as freely — and it bans the other six digits from the diagonal entirely. Both facts ripple into the rows, columns and boxes the diagonal crosses. Pinning down which three values a diagonal uses is usually the key to the whole puzzle.

Solving strategy

  • Identify the three values early. As soon as three distinct digits appear on a diagonal, every other cell on it is limited to those three.
  • Use the three-times count. Each chosen value appears exactly three times on the diagonal — no more, no less.
  • Exploit the ban. The six unused digits are forbidden from the diagonal, tightening the crossing units.
  • Feed the grid. Each diagonal digit placed behaves like a given for its row, column and box.

Common mistakes

  • Allowing a fourth value. Once three distinct digits are on the diagonal, no other may join them.
  • Forgetting the box rule. The three copies of a value must still land in different rows, columns and boxes.
  • Confusing it with X-Sudoku. X-Sudoku wants all nine different on a diagonal; Anti-Diagonal wants only three.
  • Ignoring both diagonals. The rule applies to each main diagonal separately.

Can I play it here?

Not yet — Anti-Diagonal 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: