Linear Arrangement

At a glance 9 rules

1. 1Facing decides left, rightNumber the seats from the west end. Facing north, a person's left is the west end; facing south, or facing you as in a photo, their left is your right.
2. 2Fixed seats firstPlace clues that name a seat first: an end, 'third from the left', 'only two sit left of X' (X is third). Then join people to them; use 'not next to' last.
3. 3Read the exact words'Left of' allows any gap; 'immediately left' and 'next to' mean adjacent, and 'next to' does not say which side. 'k people between' puts the seats $k + 1$ apart.
4. 4Glue chains into blocksChained clues (B just left of C, C just left of D) make one block BCD. Slide it only into a run of free seats long enough to hold it.
5. 5Run both casesWhen a clue allows two seats ('at one of the ends'), draw both rows and test every clue on each. A case dies when a count runs past an end.
6. 6Check before you answerIf two rows pass every clue, answer only what is the same in both. If the asked seat differs between them, the answer is 'cannot be determined'.
7. 7Mixed facingWhen some face north and some south, read each clue from the named person's own facing. A count that would run off the row shows which way they face.
8. 8Parallel rowsTwo rows facing each other face opposite ways, so their lefts point to opposite ends. 'Faces X' means the person directly across, same seat number from the west.
9. 9Two details per personWhen each person also has a drink, colour or job, keep one grid: seats across, with a line for names and a line for the detail. Place the detail with the tightest clues first.