# A challenging Venn diagram problem

[note: written up super fast without any editing]

We did this project with the boys last week before they went to camp for a week. Unfortunately I never got around to writing it up – here it is fairly quickly.

First we talked through the problem (again, sorry for the camera focus at the beginning – lasts 10 seconds). I wanted to go slowly introducing the problem because it is easy to go wrong right at the beginning in these problems:

In the second part we start in on the solution of the problem. My younger son takes the lead by finding how many students take only calculus. After that we spend a few minutes making sure that we know how to count the students in the various different buckets. They adopt a strategy of counting what we know and then using that information to help us find what we don’t know. By the end of this video we have found that we have 105 people to fit into the two open buckets, and we have an expression for one of those empty buckets in terms of x.

We start off this section by finding an expression for the number of people in our last remaining buck in terms of x. We now add our two expressions involving x together to get an expression. From the last video we know that this expression has to be equal to 105. After a quick review of how we got all of this information, we find that the number of people taking physics is 110:

The last part of the project is one final review of the whole problem. I wanted to go through it one more time just to double check that both kids were able to follow all of the steps:

So maybe not our best project ever, but it was nice to see that the kids were comfortable solving a challenging problem like this one. There’s lots of information to keep track of here and I’m glad they were able to see this one to the end. After their week at camp, we’ll start in on the next section of our Introduction to Counting and Probability book tomorrow. That section is about basic counting techniques.