Online games can serve as research instruments to explore the effects of game design elements on motivation and learning. In our research, we manipulated the design of an online math game to investigate the effect of challenge on player motivation and learning. To test the "Inverted-U Hypothesis", which predicts that maximum game engagement will occur with moderate challenge, we produced two large-scale (10K and 70K subjects), multifactor (2x3 and 2x9x8x4x25) online experiments. We found that, in almost all cases, subjects were more engaged and played longer when the game was easier, which seems to contradict the generality of the Inverted-U Hypothesis. Troublingly, we also found that the most engaging design conditions produced the slowest rates of learning. Based on our findings, we describe several design implications that may increase challenge-seeking in games, such as providing feedforward about the anticipated degree of challenge.