12 schoolchildren are engaged in a circle of patriotic songs, each of them knows a few songs (maybe none). We will say that a group of schoolchildren can sing a song if at least one member of the group knows it. Supervisor the circle noticed that any group of 10 circle members can sing exactly 20 songs, and any group of 8 circle members - exactly 16 songs. Prove that the group of all 12 circle members can sing exactly 24 songs.