The solution to the 4 person problem is actually pretty simple. Let's assume that we know the answer to the 2 person problem. We have 4 persons; A, B, C and D. At first the persons guess their colour (without revealing it of course) based on their direct neighbor. So for instance:`````` A <-----> B C <-----> D `````` A and B being neighbors, they guess their colours based on the solution of the 2 persons problem. Same goes for C and D. Without loss of generality, let's assume C guesses correctly his card colour. Since he can see the cards of A and B, he knows who will guess their colour correctly. For instance, if they have the same colour, A will guess correctly, if not, then B will guess correctly. Without loss of generality, let's assume A guesses correctly his card colour. He then sees that C will guess correctly.The participants agreed beforehand that clubs and hearts are associated with 0 while diamonds and spades are associated with 1. A and C now apply the solution to the 2 person problem to guess their shape group (either (diamonds or spades) or (clubs or hearts)):`````` A B | | C D `````` It is guaranteed that at least one has guessed the shape group correctly. Since they both guessed correctly the color, it is guaranteed that one of them will guess the shape correctly.

Search: