The birthday problem with our 120-sided dice

At the end of yesterday’s project we talked about how many rolls of our 120-sided dice  it should take for us to see a duplicate number:

120-Sided Dice

Today we dove into that question a littler more deeply. Only a little bit more, though, as this was just a quick 10 minute project before the kids headed off to school.

We began by reviewing the question and then spending a bit of time talking about how you would even approach a question like this one. Eventually we landed on the complimentary counting approach:

Next we moved to Wolfram Alpha to look at the expected results with different numbers of rolls (and sorry if the screen grab for this video looks terrible, not sure what happened with the upload, but the video itself is fine):

I’m happy to say that my younger son didn’t quite believe the numbers and insisted on rolling the dice a few times after we finished up just to see what was going on.

So, a fun (and quick) project. One other fun thing personally with this particular project is that many years ago I had to study 10-sided dice really carefully. It is sort of a long story, but this video tells part of it 🙂