## Code name generator

Several months ago I updated the list of words and frequencies of occurrence that I’ve used in various natural language processing experiments (keyword search “ngrams”) over the years, to reflect last year’s update to the Google Books Ngrams dataset. This … Continue reading

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## Expected length of a soccer penalty shootout

The U.S. women’s soccer team recently beat the Netherlands in a penalty shootout, soccer’s version of an overtime tie-breaker. Teams alternate turns attempting a penalty kick, resulting in either a scored point or a block/miss, and after each team has … Continue reading

## Counting collisions

Here is an interesting problem that I saw recently, that involves a nice combination of physics, programming, and mathematics, with a surprising solution. Imagine two balls on a frictionless floor near a wall, as shown in the figure below. The … Continue reading

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## Beware the “natural” quaternion

Introduction Rotation math can be confusing. But it didn’t need to be this confusing. I think the reason that 3D rotations can be tricky to work with is that there are so many choices of convention– in interpretation, notation, and … Continue reading

## Analysis of Evil Hangman

Introduction This is a follow-up to the previous post that briefly mentioned the game of Hangman, in the context of developing a dictionary of words sorted based on their frequency of occurrence in the recently updated Google Books Ngram dataset. … Continue reading

## An updated Google Books word frequency list

Introduction I think I nerd-sniped myself. This started with the objective of writing a simple program to play Hangman, as a demonstration of a potential programming exercise for students. (Don’t assign the problem if you don’t know the solution.) But … Continue reading

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## Balanced clock hands

Given an analog clock with sweeping hour, minute, and second hands, at what times are the hands most evenly “balanced”– that is, most equally separated in angle? It’s a standard high school algebra problem to compute all of the times … Continue reading

## What is the probability of a tie vote?

This article was discussed on Reddit. It is time to vote for a new mathematics department chair. All voting faculty members are on the ballot as eligible candidates… but no one really cares about the job, so each faculty member … Continue reading

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## Counting edge-matching puzzles

I recently re-discovered a puzzle that I had mostly forgotten from when I was a kid. The problem is simple to state: rearrange and rotate the seven hexagonal pieces shown below so that each of the twelve pairs of facing … Continue reading