Working with the shared assumption that mathematics itself is driven by the activity of problem solving, the purpose of our talk will be to demonstrate that any answer to the question of what makes a mathematical problem a good one must be driven by mathematical examples of problem solving. To this end, each speaker will present an example of a mathematical problem with the aim of drawing out those ingredients that seem to make it a good one. Having each presented our ingredients we will next consider that extent to which these ingredients are shared or distinct, and we will also consider whether these similarities and difference are mathematically, historically or philosophically motivated. Finally, we will offer up questions for the audience to consider. Forexample, the question of whether the ingredient of “fruitfulness” is a mathematical notion or an aesthetic one.