# Venn diagram problems

We’ve made it all the way to day 2 of our summer project working through Art of Problem Solving’s Introduction to Counting and Probability! Today’s topic was Venn diagram problems. Though both kids have seen these kinds of problems previously, it was still a worthwhile review. The difference between phrases like “at least 2” and “exactly 2” can be challenging for kids to understand.

I picked one of the problems from the “Challenge problem” section at the end of the chapter for our video today. The problem is a fairly typical Venn diagram problem. After struggling with a few of the examples today, they came up with a pretty clever solution to this one. Hopefully the earlier struggles help get the concepts to sink in (and, oh goodness, sorry for the focus problems at the beginning of the video, goes away after about 15 seconds. Yikes!):

After finding an answer to the problem, I wanted to go back through and double check the answer as a way to reinforce some of the basic Venn diagram concepts.

So, a pretty productive day today. At the start of the day both kids had a little trouble understanding how to deal with the overlapping regions in the diagrams. By the end of the morning they seemed to be pretty comfortable with the basic ideas. Hopefully thinking through problems like these helps them develop a good base to build on as we move to slightly more complicated counting problems.