The exact information complexity of Indian poker

Suppose N people are in a circle and each has a K-bit integer on his forehead and can see the others’ integersht does not know his own. How many bits of information must be exchanged among the players so that each can determine his own number after the exchange? We provide an algorithm for which bits suffice. In particular if N > K , the total of NK bits can be resolved in K + 1 transmissions. Since K bits are required to resolve any of the numbers, this is quite efficient, and is shown to be optimal. In addition the optimal strategy is obtained when the numbers are of different lengths.