To give some intuition as to why these answers are "obviously" correct; for the 2-person case you have 4 possible results: (Ava, Bob) -> (B, B), (B, R), (R, B)

To give some intuition as to why these answers are "obviously" correct; for the 2-person case you have 4 possible results: (Ava, Bob) -> (B, B), (B, R), (R, B), (R, R) It's easy to see that there are only two alternatives: they either both have the same suit or they have different suits. Luckily, there are two players, and so they can try both options simultaneously. The same thing works in the 4-player case. You can try 4 strategies at once, is there any way to somehow reduce the state space to 4 options? If you give every suit a number from 0-3, then the sum of all the suits is obviously going to be somewhere between 0-3 modulo 4.