What are the rules of Sandwich Sudoku?

Everything you know from classic Sudoku still applies. Each row, each column, and each 3×3 box must contain the digits 1 through 9 exactly once - No repeats anywhere. This layer matters more than it might seem, because it guarantees that every row and every column contains exactly one 1 and exactly one 9. That guarantee is what makes the sandwich clues well-defined: in any line there is always a unique pair of 'bread' cells (the 1 and the 9) with a unique set of cells between them. Without the standard layer, the sandwich clue would be ambiguous. With it, every outside number refers to one specific stretch of cells - You just don't know which stretch yet.

Outside each row (to its left) and each column (above it) sits a clue number. That clue equals the sum of all digits strictly between the 1 and the 9 in that line. Three details to internalise:

• The 1 and the 9 are the bread, not the filling - They are never included in the sum.
• It does not matter whether the 1 or the 9 comes first; the clue counts whatever lies between them in either order.
• The digits between them can only be drawn from 2-8, so every clue ranges from 0 (nothing between) to 35 (all of 2+3+4+5+6+7+8).

A few facts follow directly from the rules and drive all sandwich strategy. A clue of 0 means the 1 and 9 are adjacent. A clue of 35 means all seven other digits sit between them, forcing the 1 and 9 to the two ends of the line. And because a full line sums to 45, the digits outside the sandwich always sum to 45 − 1 − 9 − clue = 35 − clue. Every clue is really two clues: one for the inside of the sandwich and one for the outside.