如何遊玩 對角線數獨
兩條主對角線也必須包含1–9
Diagonal Sudoku — often printed as Sudoku X — is the variant most likely to fool you into thinking nothing has changed. The grid looks identical to a classic puzzle; the only addition is that each of the two main diagonals must also contain 1 to 9 exactly once. That single sentence rewires the whole board. Seventeen cells suddenly live in four houses instead of three, and the centre cell answers to five. It has been a world championship staple for decades precisely because of this stealth: solvers who forget to scan the diagonals stall on puzzles that are, with the diagonals, almost gentle. It's the ideal first variant for a competent classic player — no arithmetic, no new symbols, no notation to learn, just one new habit to drill until it's automatic. And easy diagonal puzzles are genuinely easier than their classic counterparts, because two extra houses means two extra sources of free eliminations. The difficulty curve only bites later, when setters start hiding the key deduction on the diagonal you stopped checking.
規則
適用標準數獨規則： 填滿每一行、列和3×3宮，數字1–9各出現一次。
在對角線數獨中，標準的9×9規則適用——但有一個強大的額外約束：兩條主對角線（左上到右下，以及右上到左下）都必須各自包含數字1到9恰好一次。這個額外約束通常使謎題更容易解決，因為對角線充當了兩個額外的刪除單元。
如需了解此謎題的來源、與相關變體的比較及策略摘要，請參閱我們的 對角線數獨變體概述.
一覽
如何解 對角線數獨
工作範例：打開一個 對角線數獨 謎題
Take the diagonal running from r1c1 down to r9c9, and suppose the givens already place 2, 4, 5, 7, 8, and 9 somewhere along it. Only 1, 3, and 6 are missing, and only three diagonal cells are empty — say r2c2, r5c5, and r6c6. Now check the centre cell r5c5 against its other houses: if row 5 already contains a 1 and box 5 already contains a 6, then r5c5 can be neither — it must be 3. That placement is invisible to anyone scanning only rows, columns, and boxes, because those houses still allowed several candidates. With 3 placed, r2c2 and r6c6 form a naked pair of {1,6} on the diagonal. Suppose column 2 already holds a 6: then r2c2 is 1 and r6c6 is 6, and the whole diagonal is done. Notice the knock-on effects: that 6 at r6c6 now eliminates 6 from the rest of row 6, column 6, box 5 — and from the other diagonal if r6c6 had sat on it. Every diagonal placement pays out in four houses, which is why the diagonals are always the right place to start.
對角線數獨中的常見錯誤
| 錯誤 | 如何修正 |
|---|---|
| Forgetting the diagonals exist after the first few minutes | Add both diagonals to your scan rotation permanently: rows, columns, boxes, diagonal, anti-diagonal. After every placement on a diagonal cell, check both diagonals before moving on. |
| Applying the diagonal constraint to cells that aren't on a diagonal | Only 17 of the 81 cells carry the extra rule — the two 9-cell diagonals, sharing the centre. Marking the diagonals visually (most apps shade them) prevents phantom eliminations. |
| Underusing the centre cell | r5c5 sits in five houses: row 5, column 5, box 5, and both diagonals. It is the most constrained cell on the board, and the digit there eliminates across all five — check it early and often. |
常見問題
什麼是 Diagonal Sudoku？ ▾
Diagonal Sudoku adds two extra constraints on top of standard Sudoku: both main diagonals of the 9×9 grid must each contain the digits 1–9 exactly once. This means every cell on either diagonal belongs to four uniqueness groups simultaneously: its row, column, box, and diagonal.
Which cells are on the diagonals? ▾
The main diagonals run from the top-left corner to the bottom-right corner, and from the top-right corner to the bottom-left corner. Together they cover 17 cells (the centre cell is on both). Any cell at position (r, c) is on a diagonal if r equals c or if r + c equals 10 (using 1-based numbering).
How does the diagonal constraint help solving? ▾
Diagonal cells carry four constraints instead of the usual three, making them the most restricted cells on the board. Whenever you place a digit anywhere on a diagonal, it eliminates that digit from the entire row, column, box, and the diagonal simultaneously — often triggering a cascade of placements.
Is Diagonal Sudoku harder than regular Sudoku? ▾
At easy difficulty, Diagonal Sudoku is actually easier than equivalent classic Sudoku because the extra constraints eliminate more candidates immediately. At hard and expert levels, the diagonal interactions create subtler deductions that experienced players find more challenging to spot.
Can I solve Diagonal Sudoku using standard techniques? ▾
Yes — all standard Sudoku techniques (naked pairs, hidden singles, pointing pairs, X-Wings, etc.) apply. You simply treat each diagonal as an additional house. The most important habit is scanning both diagonals after every placement, the same way you scan rows, columns, and boxes.
How long does Diagonal Sudoku take to solve? ▾
Easy puzzles take 5–12 minutes — often faster than equivalent classic puzzles because of the extra constraints. Medium puzzles run 12–25 minutes. Hard and expert puzzles can take 30–70 minutes depending on how heavily the diagonal interactions need to be exploited.