How to Play Sandwich Sudoku
Clues give the sum of digits between the 1 and 9 in each row/column
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.
The Rules
Standard Sudoku rules apply: fill every row, column, and 3×3 box with the digits 1–9, each appearing exactly once.
Sandwich Sudoku places clues along the outside of the grid. Each clue gives the sum of all digits squeezed between the 1 and the 9 in that row or column. The positions of 1 and 9 vary, so the 'sandwich' can have 0 to 7 cells depending on where they land. A clue of 0 means 1 and 9 are adjacent. A clue of 35 means all digits 2–8 are between them.
At a Glance
How to Solve Sandwich Sudoku
Worked Example: Opening a Sandwich Sudoku Puzzle
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.
Common Mistakes in Sandwich Sudoku
| Mistake | How to fix it |
|---|---|
| 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. |
Common Questions
What is Sandwich Sudoku? ▾
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.
What does a sandwich clue of 0 mean? ▾
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.