• ### Snowplow Riddler

In this post, I will walk through a solution to last week’s Riddler from FiveThirtyEight, which concerns a snowplow clearing snow. We are told some details about how the snow falls and how the snowplow clears the snow, and then we are asked (somewhat counterintuitively): when did it start snowing?

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• ### Markovian Dice Riddler

In this post, I explore a solution to FiveThirtyEight’s Riddler problem from March 27th. In this problem, we are asked to consider a process in which we repeatedly roll a fair die in batch rounds of size equal to the number of sides on the die. After each round, the die is relabeled using the outcomes of the batch’s rolls. Eventually, all faces of the die will receive the same label and we’re asked: on average, how many rolls will it take before the die’s faces are all the same?

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• ### Markovian Ducks Riddler

Two Friday’s ago, the FiveThirtyEight Riddler problem asked us to consider some ducks stochastically swimming between rocks in a pond. We are told that initially the ducks are sitting together on a rock in the middle of the pond, and each minute all of the ducks will independently randomly swim to one of their neighboring rocks with equal probability. We are told to assume that the rocks are laid out in a square grid, and that the ducks only swim horizontally and vertically. Assuming $$2$$ ducks on a $$3 \times 3$$ grid, the prompt asks us: how long on average will it take for all of the ducks to land together on the same rock?

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• ### US State Hamiltonian Path Riddler

FiveThirtyEight’s Riddler problem for last week asked if it was possible to take a road trip in which you visit every continental US state without ever having to cross over the same border more than once - although returning to the same state is allowed. In this post, I’ll show that this in fact possible, and I’ll also provide a solution which only passes through each state exactly once.

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• ### Rubik's Cube Project Write-Up

Over the past few weeks, I’ve been working on a developing a program to assist the solution of a Rubik’s cube. The project started as an elaborate “joke,” after I messed up a friend’s Rubik’s cube and couldn’t put it back into its solved state. The goal of this project is to read in the state of an unsolved Rubik’s cube from a camera feed (or set of static images), and to provide step-by-step graphical instructions on how to solve the Rubik’s cube. Roughly, the project breaks down into four steps:

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