Struggling thorough a challenging counting problem

I tried a pretty tough counting problem with the boys last night. For the first part of our discussion they were accidentally heading down the wrong path without realizing it. It is a good lesson on how easy it is to accidentally count the wrong thing.

Here’s the problem:

How many 4 digit integers are missing at least one of the digits 0 and 1?

Here’s the introduction to the problem and the walk down the wrong path:

At the end of the last video we came to the conclusion that we’d gone wrong. Our guess was around 700, but the answer definitely had to be bigger than 4,000. What happened?

I think the process we went through here is a good lesson – it is really easy to count the wrong thing by accident. You don’t always get as lucky as we did here and count *exactly* the wrong thing!, though. But it still is nice to see how going back and reviewing your solution can help you get back on the right track.