I’ve been involved in a number of conversations where discussing a problem ad nauseum is maybe not what the situation requires.
One notable instance was, while waiting in line for a buffet in Vegas, a friend and I were discussing if it was possible that for some combination of number of players and initial state of a deck of cards that a game of war could reach a state where it never completed. That is to say, some sequence of wars would just continue looping with no clear victor.
I think we reached the conclusion that this was possible, but didn’t get any good ideas on how to prove it one way or another before it was time to eat. (The other people in our group were glad when we finally shut up about war.)