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A query game is a pair of a set $Q$ of queries and a set $\mathcal{F}$ offunctions, or codewords $f:Q\rightarrow \mathbb{Z}.$ We think of this as atwo-player game. One player, Codemaker, picks a hidden codeword $f\in\mathcal{F}$. The other player, Codebreaker, then tries to determine $f$ byasking a sequence of queries $q\in Q$, after each of which Codemaker mustrespond with the value $f(q)$. The goal of Codebreaker is to uniquely determine$f$ using as few queries as possible. Two classical examples of such games arecoin-weighing with a spring scale, and Mastermind, which are of interest bothas recreational games and for their connection to information theory.  In this paper, we will present a general framework for finding shortsolutions to query games. As applications, we give new self-contained proofs ofthe query complexity of variations of the coin-weighing problems, and prove newresults that the deterministic query complexity of Mastermind with $n$positions and $k$ colors is $\Theta(n \log k/ \log n + k)$ if only black-peginformation is provided, and $\Theta(n \log k / \log n + k/n)$ if both black-and white-peg information is provided. In the deterministic setting, these arethe first up to constant factor optimal solutions to Mastermind known for any$k\geq n^{1-o(1)}$.

Optimal schemes for combinatorial query problems with integer feedback