Cross off what cannot be true
Work out who has what from a handful of clues. Every puzzle here has exactly one answer, every clue is needed, and none of it requires a guess.
Click a cell to mark it a definite yes; click again for a definite no. Marking a yes crosses off the rest of its row and column automatically.
How the clue list is trimmed to exactly what is needed
An arrangement is chosen first, then described truthfully in far too many clues — every direct link, a spread of negatives, and every comparison the ordinal category allows. That set certainly determines the answer, and it is also unreadable.
So clues are removed one at a time. Each candidate is taken out and the remaining set re-solved from scratch; if exactly one arrangement still fits, that clue was never load-bearing and stays out. What survives is a set where every clue matters — take any one away and the puzzle becomes ambiguous. That is asserted by the tests rather than assumed.
Two further checks before publishing. Exactly one arrangement must fit, because a logic puzzle with two answers is much easier to produce by accident than a broken one — dropping one clue too many usually leaves a symmetric pair rather than something obviously wrong. And the puzzle must be solvable by elimination alone, with no guessing, or it is discarded.
The order clues are offered for deletion decides the puzzle's character, and it is the reverse of what it looks like: a clue offered early is the one removed. Easy offers comparisons first, so direct links survive; hard offers links first, so comparisons survive.
How to work one of these
The grid pairs every category with every other. A dot means "these two definitely go together"; a cross means "these two definitely do not". Marking a dot immediately crosses off the rest of that row and column, because each item belongs to exactly one entity — and that automatic step is where most of the progress comes from.
The move people miss is the indirect one. If A definitely has X, and a clue says the one with X does not have Y, then A does not have Y either — even though no clue mentions A and Y together. Chasing those consequences through the grid is the whole game.
Comparisons carry more than they look like
"Finished before" or "two higher than" does more work than a direct link, because it constrains both ends at once and rules out the extremes. If the one in red finished before the one in blue, red cannot be last and blue cannot be first, and that is often the first real foothold on a hard puzzle.
Related
Nonograms for elimination on a picture, and Sudoku for the same on numbers.
Questions people actually ask
Is every clue actually needed?
Yes, and it is enforced rather than hoped for. Clues are generated in surplus, then removed one at a time — each candidate is taken out and the remaining set re-solved from scratch, and it only stays out if exactly one arrangement still fits. What ships is a set where removing any single clue makes the puzzle ambiguous.
Can there be two answers?
No. Solutions are counted with the search stopping at two, and a puzzle is discarded unless exactly one arrangement fits. This matters more here than in most puzzles: dropping one clue too many usually leaves a neat symmetric pair of answers rather than something obviously broken.
Do I ever have to guess?
Never. Before publishing, the puzzle is solved by constraint propagation alone — the same crossing-off you do on the grid — and discarded if that is not enough. If you are stuck, there is a deduction available.
Why does marking a yes cross off other cells?
Because each item belongs to exactly one person, so a confirmed pairing rules out everything else in that row and column. Doing it by hand is the tedious part of these puzzles and adds nothing, so it happens automatically.
What makes hard puzzles harder?
Which clues survive the trimming. Easy puzzles keep direct links — 'Carmen has stall 1' — which settle a cell immediately. Hard puzzles keep comparisons instead, which constrain both ends at once and only pay off once combined with something else.
Where do the names and themes come from?
They were written for this. The brief this was built to forbids scraping puzzle banks and word lists, and four short themed sets are easy enough to write that there was no reason to take them from anywhere.