In a class of 29 students 15 students have cats and 20 have dogs How many students have both cats and dogs?

Short answer: Anywhere from 6-15 students will have both a cat and a dog. The maximum number that can have both is 15, if each student who has a cat also has a dog. To find the minimum number, we must try to get as many students to only have one pet as possible. Let's take students 1-20 and give them dogs. Now give the last 9 students cats. We still have 6 (15-9) cats left to distribute and no places to put them. This means that at least 6 students need to have both a cat and a dog.