"Mathematics" Posts
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Aiming Projectiles
Shooting is a very common mechanic in video games; however, unless your projectiles are entirely hitscan—meaning that the player instantly hits whatever they are aiming at when pulling the trigger—aiming projectiles is unexpectedly non-trivial from a mathematical perspective. For players, this is part of the fun, and their aim is more driven by physics intuition and muscle memory. But for AI-controlled characters, this is a real problem, and there are a number of factors that can potentially make it even more complicated. In this post, I will be discussing the solutions for the most common category of projectile aiming problems in video games.
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Corner Place
The puzzles I’ve posted so far have been easy-to-describe as “like sudoku, but…”. But, as I’ve done more research into the mathematics underlying these types of puzzle systems, I’ve come to realize that the “sudoku-like”ness of these puzzles is captured entirely by the concept of the “Latin square”. And, in doing further research into Latin squares, I found a neat kind of puzzle that seems very underexplored.
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Triple Place
A few months ago, I started posting a daily puzzle called Pair Place. Pair Place arose naturally as a math problem during some research, but I naturally started to wonder if there were any basic generalizations of it that could serve as variations on the same puzzle concept. The first such generalization of Pair Place is the subject of today’s post: Triple Place.
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Pair Place
I thought that it might be a good challenge to try to introduce and keep up-to-date a daily puzzle on the site for as long as I can manage. So, starting today, I will be uploading a daily puzzle for a puzzle system I’ve been investigating, which has some similarities to sudoku.
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