X-Sudoku, also called diagonal Sudoku, is standard Sudoku with one extra rule. As well as each row, column and 3 by 3 box containing 1 through 9 once, both main diagonals must also contain 1 through 9 exactly once. The two diagonals form an X across the grid.

How is X-Sudoku different from regular Sudoku?

The grid, the digits and the row, column and box rules are identical to regular Sudoku. The only difference is the added constraint that both main diagonals must each contain 1 through 9 once. That gives you extra lines to scan and extra eliminations to make, so the diagonals are both the challenge and the gift.

What is the best strategy for X-Sudoku?

Treat each diagonal as an extra row or column. Whenever you place a digit on a diagonal, eliminate it from the rest of that diagonal. Start with the centre cell, which sits on both diagonals plus its row, column and box, making it the most constrained cell on the board and often the first you can solve.

Does solving X-Sudoku ever require guessing?

No. A well-made X-Sudoku has exactly one solution reachable by pure logic. Every Puzzle Lair X-Sudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often one hiding on a diagonal.

Is X-Sudoku harder than regular Sudoku?

At the same stated difficulty the extra diagonal constraint usually makes X-Sudoku faster to crack, because it gives you more ways to eliminate candidates. The hard set is where the diagonals bite back, demanding that you track all four units, row, column, box and diagonal, for the trickiest cells.

Solving guides

From the rulebook

How to Solve X-Sudoku

X-Sudoku, also called diagonal Sudoku, keeps every rule of standard Sudoku and adds one more: both main diagonals must also contain 1 through 9. That extra constraint gives you more deductions, not fewer, once you know how to use it. This guide takes you from the rules to the techniques that crack hard diagonal grids.

Play X Sudoku

The rules of X-Sudoku

An X-Sudoku is a 9 by 9 grid split into nine 3 by 3 boxes, exactly like standard Sudoku. Some cells start filled with given digits. Your job is to fill every empty cell so that each row, each column and each 3 by 3 box contains the digits 1 through 9 exactly once.

On top of that, both main diagonals, the one running top-left to bottom-right and the one running top-right to bottom-left, must also contain the digits 1 through 9 exactly once. The two diagonals form an X across the grid, which is where the puzzle gets its name.

Start by scanning

The fastest opening move is scanning. Pick a digit, say 5, and look across the rows, columns and boxes where a 5 already appears. Those lines and boxes cannot take another 5. Often that leaves only one empty cell in a box where a 5 can legally go, so you can place it with certainty.

Work digit by digit through the grid. Scanning alone solves most easy puzzles and gives you a strong head start on medium ones. In X-Sudoku, also scan the two diagonals as if they were extra lines, a digit already on a diagonal blocks the rest of that diagonal.

Treat the diagonals as extra lines

The single biggest habit for X-Sudoku is treating each diagonal exactly like a row or column. Whenever you place a digit on a diagonal cell, immediately eliminate that digit from every other cell on the same diagonal. Many placements that look impossible by row, column and box logic alone become forced once you add the diagonal.

The centre cell sits on both diagonals plus its row, column and box, making it the most constrained cell on the entire board. Check it early. The four cells diagonally adjacent to the centre, and the four corners, also each carry a diagonal constraint, so they tend to resolve sooner than ordinary cells.

Use pencil marks for candidates

When scanning stops finding placements, switch to pencil marks. In each empty cell, note the small candidate digits that could still legally go there. As you fill cells, erase candidates that are now blocked. A cell left with a single candidate is a forced placement.

For cells on a diagonal, factor the diagonal into the candidate list as well as the row, column and box. Diagonal cells usually carry fewer candidates than their neighbours, which makes them the best place to look for single candidates and naked pairs.

Naked pairs, hidden pairs and pointing pairs

A naked pair is two cells in the same row, column, box or diagonal that share the same two candidates, for example both holding only 3 and 7. One must be the 3 and the other the 7, so you can remove 3 and 7 from every other cell in that unit. In X-Sudoku the diagonals count as units too, so a naked pair on a diagonal clears candidates along the whole diagonal.

Pointing pairs and box-line reduction work the same as in standard Sudoku, and you apply techniques in the same order: easy scans first, then pencil marks, then pairs and pointing pairs, always re-checking the diagonals as you go. On Puzzle Lair every X-Sudoku is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess.

Frequently asked questions

What is X-Sudoku?: X-Sudoku, also called diagonal Sudoku, is standard Sudoku with one extra rule. As well as each row, column and 3 by 3 box containing 1 through 9 once, both main diagonals must also contain 1 through 9 exactly once. The two diagonals form an X across the grid.
How is X-Sudoku different from regular Sudoku?: The grid, the digits and the row, column and box rules are identical to regular Sudoku. The only difference is the added constraint that both main diagonals must each contain 1 through 9 once. That gives you extra lines to scan and extra eliminations to make, so the diagonals are both the challenge and the gift.
What is the best strategy for X-Sudoku?: Treat each diagonal as an extra row or column. Whenever you place a digit on a diagonal, eliminate it from the rest of that diagonal. Start with the centre cell, which sits on both diagonals plus its row, column and box, making it the most constrained cell on the board and often the first you can solve.
Does solving X-Sudoku ever require guessing?: No. A well-made X-Sudoku has exactly one solution reachable by pure logic. Every Puzzle Lair X-Sudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often one hiding on a diagonal.
Is X-Sudoku harder than regular Sudoku?: At the same stated difficulty the extra diagonal constraint usually makes X-Sudoku faster to crack, because it gives you more ways to eliminate candidates. The hard set is where the diagonals bite back, demanding that you track all four units, row, column, box and diagonal, for the trickiest cells.

Ready to play? Start a X Sudoku puzzle