Seven kids (siblings Alex and Beth, siblings Cindy and Denise, siblings Effie and Fred, and lone child George) got into trouble over one or more Hallowe’en “events”. A kid is “nicer” than another kid if the first kid was involved in fewer events. “worse” is the opposite. The events were collecting candy twice, setting off firecrackers, and stomping on a geezer’s lawn. There are eight combinations of events, but none of these kids are angels so ignore the no events possibility. Each kid was responsible for a different combination.
Alex is nicer than Denise. No two siblings both set off firecrackers. Beth is worse than Denise. Effie set off firecrackers. Alex and Fred went lawn stomping, but Denise did not. No two siblings are equally nice.
So who did what?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 11, 2015 at noon Pacific Time. I will post the answer shortly after.