I’m having a few problems with parsing the new quiz…
1) Tim is asked, “Are there more than two players who have the same total?” He answers, “Yes.”
There are four totals, including yours (which you don’t know). The other totals are: Jeff: 2+4+8 = 14 Tim: 4+5+8 = 17 Mike: 1+5+5 = 11
For Tim to know that more than two players have the same total, all three of you, Jeff, and Mike would have to have the same total. This is impossible, so either Tim is a lying cheat or the Quiz has an issue.
2) Jeff asks how it’s possible that both Tim and he have an 8 of spades, but he shouldn’t be able to see his own cards, so how would he know? Only “you” and Mike should be able to ask that question, and you already understand the multiple deck concept. Was the question meant to be asked by Mike, or is Jeff also a lying cheat?
3) Tim interrupts that he knows what he has, but you then contemplate that Jeff is a smart guy and wouldn’t bluff. Was it meant to be Jeff that interrupted? It seems unlikely to be either, as they have each only learned one new piece of information each while Mike and you have each gained two (one each from Tim and Jeff’s answers).
I think two and three could be resolved if Mike asked the question about different even numbers and commented that Tim and Jeff both have eights of spades, then Jeff announced that he knows his cards. Still can’t reconcile the first question, though.