The Monty Hall Dilemma (MHD) is a classic brain teaser that even mathematicians appear to consistently answer incorrectly, and when the correct solution is presented people remain unconvinced. We examined how convincing were three solution types: a simple statement of the solution, a guided diagram solution, or simulated trials. Participants were given the MHD, followed by one of the three types of solutions, then we measured their level of conviction and their numeracy, Cognitive Reflection (CR), Need for Cognition (NFC), and Openness. Overall, both guided diagrams and simulated trials led to higher conviction compared to a simple solution statement. Higher numeracy and higher CR were associated with lower conviction after the simple solution; furthermore higher numeracy tended to help more in the simulation condition, whereas higher CR helped more in the guided condition. Therefore the persuasiveness of a solution depended both on its nature and characteristics of individual reasoners.