What does a clue of 35 mean?
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35 is the largest possible sandwich clue, and like the 0 clue it removes all ambiguity about the shape of the sandwich. Every digit other than the bread itself must be inside - So the bread goes to the ends of the line.
The Math Behind 35
The digits available to fill a sandwich are 2, 3, 4, 5, 6, 7, and 8 - The 1 and 9 are the boundaries and digits cannot repeat in a line. Those seven digits sum to 2+3+4+5+6+7+8 = 35. A clue of 35 therefore requires every one of them to be inside the sandwich: seven sandwiched cells plus the two bread cells accounts for all nine cells in the line. The only way to fit that is with the 1 and 9 in the first and last cells. No other clue value forces the full span, and 34 is impossible altogether - Dropping any digit from the full set loses at least 2.
What a 35 Clue Gives You
Immediately mark the two end cells of the line with the candidate pair {1,9} and remove 1 and 9 as candidates from the seven interior cells. That is a naked pair on the line's endpoints: any other line or box containing one of those end cells can no longer place its own 1 or 9 freely there. Deciding which end holds the 1 and which holds the 9 usually comes from the crossing clues - The column through one end cell may be unable to accommodate a 9 in that position, settling both ends at once.
Near-Maximum Clues Are Almost as Good
A clue of 33 deserves the same respect. Six sandwiched cells summing to 33 means exactly one digit from 2-8 is outside the sandwich, and it must be 35 − 33 = 2. So the 1 and 9 sit seven cells apart - Positions (1,8) or (2,9) - And the single leftover cell holds the digit 2. The same logic gives clue 27 a leftover digit of 8. High clues compress the geometry of the line nearly as hard as 35 itself.