• Infinite Chain Link Riddler

    In this post, I will walk through my solution to the most recent Riddler problem. Here, we are asked to determine the path that is traced out by the tail end of a certain rigidly moving finite length chain with infinitely many links. While the behavior of each individual link in the chain is fairly complex, the path traced by its tail is surprisingly simple! (Although maybe this shouldn’t have been surprising! 🙂)

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  • Analyzing Error in Buffon's Needle Problem

    A few months back, I began writing up a simple visualization in D3 to illustrate Buffon’s needle method for approximating \(\pi\) for a post celebrating Pi Day. The visualization took me a bit longer to complete than I had anticipated, so I ended up shelving the post at that time. However, while playing with the simulation, I noticed that the approximations to \(\pi\) from this method aren’t especially good. To quantify just how bad this approximation is, I worked out an asymptotic error analysis of this estimator. In this post, I have included my completed visualization along with the error analysis. For good measure, I also ran a Monte Carlo study of the error in Julia 🙂

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  • Random Election Upsets Riddler

    In this post, I’ll discuss the Classic Riddler problem from April 23rd 2021, which asks us to consider a large nation of voters who independently submit their vote between two candidates (A and B) by flipping identical fair coins. We’re asked: if 80% of votes are tallied on election day (regular votes), while the remaining 20% (early votes) are tallied later, what is the probability of an upset – i.e. what is the probability that the election day outcome doesn’t match the final outcome?

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  • Stochastic Streets Riddler

    In this post, I describe my (lazy) solution to FiveThirtyEight’s most recent Riddler Problem. This problem asks us to imagine living in a city which has a square gridded network of one-way streets whose orientations were assigned completely at random. Supposing that you live in the upper left corner of the city and work in the lower right corner, we’re asked: How likely is it that you can navigate from your home to work via the city’s street network?

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  • Inefficient Cranberry Sauce Passing Riddler

    In this post, I’ll walk through my solution to last week’s cranberry sauce passing problem from FiveThirtyEight’s “The Riddler.” In this problem, we’re asked to consider 20 guests sitting around a circular Thanksgiving table, who all want to receive a serving of cranberry sauce. These guests are somewhat lazy/careless, and whenever a guest receives the sauce, they will randomly pass the sauce to their left or right with equal probability. The guests continue in this fashion until everyone has been served. Under these conditions, we are asked:

    1. Assuming that the sauce begins in front of a pre-specified guest, which of the remaining guests has the greatest chance of receiving the sauce last?
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