Sandwich Sudoku

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 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).

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 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.

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.