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.
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.
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.
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:
- Try the closely related X Sudoku, which you can play right now.
- Browse all the Sudoku variants we do offer.
- Or print free puzzles from the printable PDF page.
Where to play it
Anti-Diagonal Sudoku belongs to the constraint family and runs on 9×9. It is not one SudokuStreak generates yet - but the deduction it trains is the deduction every Sudoku runs on.
Difficulty and type are two separate dials here: the type sets the extra rule, the level sets how much of the grid you start with. Hard Sudoku leaves 26 of the 81 cells filled, where scanning gets you started and then leaves you stranded; Expert Sudoku leaves 25, where the beginner tools dry up almost entirely. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.