In a certain kindergarten class, the only pets students have are cats and dogs. There are exactly 9 students in the class who do not have any pets, and exactly 5 who have both kinds of pets. Solution: there are 15 students who do have at least one pet, and another 9 who don"t have any pets, which means that there must be exactly 24 students in the kindergarten class. Solution: we know that there are 17 students who don"t have any dogs. Those 17 include the 9 who have no pets, and there must be 8 others who have one or more cats but no dogs. 5 who have both kinds of pet, gives 13 students who do have at least one cat. Solution: there are 12 on the ac branch, and only 2 branches following this branch, so the numbers on these 2 branches must sum to 12.