Previous research into problem solving in physics resulted in researchers introducing six epistemic games to describe the organizational structures of locally coherent resources. We present a new epistemic game--the "answer-making epistemic game"--which was identified in this paper through the analysis of interviews carried out to validate a survey focusing on students' understanding of Archimedes' principle and Pascal's law. In the game, the ultimate goal is a solution to a problem posed by the survey. Students may remember or intuit an answer, then use conceptual and/or mathematical reasoning to justify it. Alternately, they may use conceptual and/or mathematical reasoning to generate an answer. We demonstrate how students generate their solutions using these two different paths and discuss some implications for instruction. (Contains 2 figures.)