An example Sandwich puzzle: the clue 19 above column 1 sums the digits trapped between the 1 and the 9 - 8 + 4 + 7.
Sandwich Sudoku hangs a clue outside each row and column. That clue is the sum of the digits trapped between the 1 and the 9 - the two "crusts" of the sandwich. The digits in between are the "filling", and their total is all the clue tells you. There are usually only a handful of given numbers, so learning to read these sums is the whole game.
The rule: sum the filling between the crusts
In every row and column, find the 1 and the 9. Everything strictly between them adds up to the clue; the 1 and the 9 themselves are never counted, and it does not matter which comes first. In the row below, the 1 and the 9 sit three apart with a 5 and a 7 between them, so the clue is 12.
The clue 12 is the sum between the 1 and 9 (the crusts): the 5 and 7 filling add to 12.
The two extremes: 0 and 35
Two clues are worth memorising because they place digits instantly. A clue of 0 means there is nothing between the crusts - the 1 and the 9 are next to each other. A clue of 35 is the largest possible: the 1 and the 9 sit at the two far ends of the line, with all seven of 2, 3, 4, 5, 6, 7 and 8 sandwiched between them (2+3+4+5+6+7+8 = 35).
A clue of 0 puts the 1 and 9 side by side; a clue of 35 pushes them to the two ends with 2-8 between.
Reading a sum into positions
Most clues sit between these extremes and tell you two things at once: which digits fill the sandwich and how far apart the crusts are. The filling can only ever use the digits 2 to 8 - never the 1 or the 9, since those are the crusts themselves. That has a neat consequence: a clue of 1 is impossible, because the smallest filling is a single 2. A clue of 5 is then either a lone {5} (crusts two cells apart) or {2, 3} (crusts three apart). As the clue grows, so must the gap between the 1 and the 9, which quickly limits where those two digits can live. Pair the clue with the digits already in the line and the crust positions often lock down.
A worked example, step by step
Take a row with the clue 3.
Step 0. A row with the sandwich clue 3.
Step 1 - find the filling. The filling digits (2-8) must add to 3. A single 3 does it; two cells would need at least 2 + 3 = 5, too much. So the filling is exactly one cell holding a 3, and the 1 and 9 sit on either side of it.
Step 2 - that's a three-cell block. The crust-filling-crust pattern forms an unbroken block: 1, then 3, then 9 (or 9, 3, 1). Wherever that block lands in the row, the sandwich is complete.
Step 2. The clue 3 means a solid 1-3-9 block; other clues fix where it sits.
Solving strategy
- Grab the 0s and 35s first. They place the 1 and the 9 immediately - the hardest pair of digits to pin down in most variants.
- Turn the clue into a length. Work out how many cells the filling must span, then slide that window along the line to see where it fits.
- Cross rows against columns. A crust fixed by a row clue instantly helps every column clue it crosses, and vice versa.
- Think in combinations. Which distinct digits add to the clue is the same reasoning as Killer combinations.
Common mistakes
- Counting the crusts. The 1 and the 9 are never part of the sum - only the digits strictly between them.
- Assuming an order. The 9 may come before the 1; the clue is the same either way.
- Forgetting the empty sandwich. A clue of 0 is not "no clue" - it is the powerful statement that the crusts touch.
- Ignoring the length. A clue fixes both the filling digits and the distance between the crusts; use both halves of that information.
Can I play it here?
Not yet - Sandwich 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 Killer, 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
Sandwich Sudoku belongs to the arithmetic 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. Easy Sudoku leaves 36 of the 81 cells filled, so there is always an obvious next move somewhere; Hard Sudoku leaves 26, where scanning gets you started and then leaves you stranded. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.