There are seven teacups on the table, all with their mouths up. You are allowed to turn four at a time. Can you turn them all down after a few turns?

Solution: Note that the mouth of the teacup is+1 and the mouth is-1. According to the meaning of the question, at the beginning, all seven teacups are in the state of+1, and their product is also+1. Turning four teacups at a time is equivalent to changing the sign of four of seven numbers, but changing the sign of an even factor of a product cannot change the sign of the product. Therefore, no matter how many times you operate, you can't make the product-1. When all seven teacups face down, all states are-1, and their product is-1, so it is impossible to make all seven teacups face down by operation.