Q-ary search with one lie and bi-interval queries

The following search game is considered: there are two players, say Paul (or questioner) and Carole (or responder). Carole chooses a number x*∈Sn={1,2,…,n}, Paul has to find the number x* by asking q-ary bi-interval queries and Carole is allowed to lie at most once throughout the game. The minimum worst-case number LB(n,q,1) of q-ary bi-interval queries necessary to guess the number x* is determined exactly for all integers n⩾1 and q⩾2. It turns out that LB(n,q,1) coincides with the minimum worst-case number L(n,q,1) of arbitrary q-ary queries.