Carefully observing young children at play in a mathematically rich environment has led me to reflect on the way children naturally pose and solve interesting mathematical challenges. Here, three examples of the playful learning of six-year-old children illustrate the problem solving and persistence children can display. Teachers are encouraged to foster children's problem posing by providing opportunities for children to engage with playful mathematics, planning time for children to pose and to solve their own problems, and watching and listening but intervening only to inspire children's mathematical investigations.