Question 98
Masha has an electric carousel in her garden that she rides every day. As she likes order, she always leaves the carousel in the same position after each ride. But every night three bears sneak into the garden and start turning the carousel. Bear dad turns the carousel each time by $\frac{1}{7}$ of the full circle. Bear mum turns the carousel each time by $\frac{1}{9}$ of the full circle. Bear cub turns the carousel each time by $\frac{1}{32}$ of the full circle. Every bear can turn the carousel as many times as he or she wants. In how many different positions may Masha find the carousel in the morning?