Sharing the ABRACADABRA problem with kids

Yesterday we did a fun project on Markov chains and sharing the “COVFEFE” problem with kids:

Sharing Markov chains and the “covfefe” problem with kids

For me math behind this problem was the most interesting math I learned in 2017:

The most interesting piece of math I learned in 2017 -> the “covfefe” problem

Today we moved on to a really neat surprise, and what makes the math behind this problem incredibly fun -> the “ABRACADABRA” problem.

First, we reviewed the ideas from yesterday:

After that review, we though through a few of the states and the transition probabilities in the new word. The transition probabilities are subtly different than in the “COVFEFE” problem:

Now we went to Mathematica to code in the ideas we discussed in part 2. We did about half of the coding on camera and did the other half off camera:

Finally, having finished the code we discussed what results we expected. I don’t see how anyone could get the right intuition here seeing the problem for the first time, so what do you expect here is almost an unfair question. Still, the boys had some nice ideas and then we checked out the results:

There are other approaches to these problems – the approach via Martingales, for example:

What that approach is also interesting (and incredible – you can solve the stopping time in your head!) I think the Markov chain approach is a bit more accessible to kidsd. Well . . . maybe because the math is buried in the background.

Anyway – super fun project, and an great piece of math to share with kids.

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