Cách chơi Sandwich Sudoku
Các manh mối đưa ra tổng các chữ số giữa số 1 và số 9 trong mỗi hàng/cột
Sandwich Sudoku is the newest classic in the family: it went viral in 2019 after appearing in The Guardian, and it plays unlike anything else on this site. The grid is typically near-empty; the information lives in numbers written outside each row and column, each giving the sum of the digits trapped between that line's 1 and its 9 — the "crusts" of the sandwich. Nothing about the rule is hard to state, but the solving feel is closer to algebra than to scanning: you spend the opening locating crusts, not placing digits, and a single clue can interact with the geometry of the whole line. It suits solvers who like working a puzzle from its skeleton outward — if you enjoy the moment in killer when the 45 rule cracks a box open, sandwich gives you that moment on every line. Beginners should know one comfort: only the digits 1 and 9 have special status, so once the crusts are pinned, the puzzle relaxes into friendly classic Sudoku with a head start.
Các quy tắc
Áp dụng các quy tắc Sudoku tiêu chuẩn: điền mọi hàng, cột và ô vuông 3×3 với các chữ số 1–9, mỗi số xuất hiện đúng một lần.
Sandwich Sudoku đặt các manh mối dọc theo bên ngoài lưới. Mỗi manh mối cho biết tổng của tất cả các chữ số bị kẹp giữa số 1 và số 9 trong hàng hoặc cột đó. Vị trí của số 1 và số 9 thay đổi, vì vậy 'sandwich' có thể có 0 đến 7 ô tùy thuộc vào nơi chúng đáp xuống. Một manh mối 0 có nghĩa là số 1 và số 9 kề nhau. Một manh mối 35 có nghĩa là tất cả các chữ số 2–8 ở giữa chúng.
Để biết nguồn gốc của câu đố này, cách so sánh với các biến thể liên quan và tóm tắt chiến lược, hãy xem của chúng tôi Sandwich Sudoku tổng quan biến thể.
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Cách giải Sandwich Sudoku
Ví dụ đã làm: Mở một Câu đố Sandwich Sudoku
Say row 3 has a clue of 0 — the 1 and 9 must be adjacent, with nothing between them. That alone forbids 1 and 9 from sitting at opposite ends of the row, and pairs them into a moving two-cell block: eight possible positions. Now suppose column 5 has a clue of 2. The only digits summing to 2 between a 1 and a 9 are exactly one cell containing a 2 — there is no other way, since 1 and 9 themselves can't be filling. So in column 5 the pattern is 1, 2, 9 or 9, 2, 1 vertically, three consecutive cells somewhere in the column. Cross-reference: if those three cells must include r3c5, then r3c5 is the 1, the 2, or the 9 of column 5 — but row 3's clue of 0 says row 3's own 1 and 9 are adjacent, which constrains whether a 1 or 9 can sit at c5 with its partner beside it. Suppose the geometry only works with the 2 at r3c5: you've placed a digit in a near-empty grid purely by intersecting two clues. That intersection move — row possibilities meeting column possibilities at one cell — is the entire sandwich midgame, repeated until the crusts lock and ordinary Sudoku finishes the job.
Lỗi thường gặp trong Sandwich Sudoku
| Sai lầm | Cách khắc phục nó |
|---|---|
| Including the 1 and 9 in the sandwich sum | The clue counts only the digits strictly between the crusts. A clue of 35 means digits 2–8 all sit inside, forcing 1 and 9 to the line's two ends — it does not include the crusts themselves. |
| Treating small clues as allowing many fillings | Tiny sums are nearly unique: 0 means crusts adjacent, 2 means exactly one cell holding the 2, 3 means exactly one cell holding the 3 (1 can't be filling — it's a crust). Small clues are the strongest openings on the board. |
| Working clue-by-clue instead of intersecting rows with columns | A single clue rarely places anything. Enumerate the few legal 1/9 positions per line, then look where a row's possibilities and a column's possibilities collide at one shared cell — that intersection is where digits actually land. |
Câu hỏi thường gặp
Sandwich Sudoku là gì? ▾
Sandwich Sudoku is a variant where clue numbers appear outside the grid, one per row and one per column. Each clue tells you the sum of all digits that appear between the 1 and the 9 in that row or column. Standard Sudoku rules apply throughout.
How do I use the sandwich clues? ▾
First, find the positions of the 1 and 9 in each row or column — every other digit between them must sum to the outside clue. A clue of 0 means the 1 and 9 are adjacent. A clue equal to the maximum possible sum (e.g., 35 for a 7-cell sandwich) tells you the 1 and 9 are at the ends. Work from the most constrained clues first.
Một gợi ý sandwich 0 có nghĩa là gì? ▾
A clue of 0 means no digits are sandwiched between the 1 and 9 — they must be directly adjacent to each other. This is one of the most powerful clues because it immediately tells you where 1 and 9 can and cannot be placed relative to each other in that row or column.
Is Sandwich Sudoku harder than regular Sudoku? ▾
Yes, generally. Sandwich Sudoku provides very few pre-filled digits inside the grid. Almost all deductions flow from working out where 1 and 9 can sit and what sums are achievable. The logic is more algebraic than classic Sudoku, which many players find both more challenging and more satisfying.
Can the 1 and 9 be at the ends of a row? ▾
Yes. If the 1 is in column 1 and the 9 is in column 9 (or vice versa), the sandwiched digits are columns 2–8, giving a maximum possible sum of 2+3+4+5+6+7+8 = 35. Extreme clue values like this immediately fix the positions of both the 1 and the 9.
How long does Sandwich Sudoku take to solve? ▾
Easy puzzles typically take 10–20 minutes. Medium puzzles run 20–35 minutes. Hard puzzles can take 45–75 minutes, and expert puzzles often exceed 90 minutes. The key bottleneck is working out 1/9 positions — once you pin those down, the rest of the grid often resolves quickly.