Q-ary Ulam-Rényi game with constrained lies

The Ulam-Rényi game is a classical model for the problem of determining the minimum number of queries to find an unknown number in a finite set when up to a finite number e of the answers may be lies. In the variant, we introduce in this paper, questions with q many possible answers are allowed and lies are constrained by a prescribed graph. We essentially solve the problem exact asymptotically under some symmetry-hypothesis. All our strategies are implementable by procedures which use adaptiveness only once.