In this paper, we consider a number-guessing game in which the competitor guesses numbers from several hints. If the competitor guesses at least one numbers correctly, he/she can keep on guessing the remaining incorrect numbers. We first explore the case when the hints are uniformly distributed. When the competitor has more information about the right numbers, there are different strategies to guess numbers. We study the optimal strategy in such case.
In uniform case, we use recursive method to compute the winning probability. In non-uniform case, we find that the optimal strategy is to choose the most probable hints of each number.