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Telling the tale of two tetrations
Many people are familiar with exponential growth. We use it to model many things, including compounding interest and viral spread. To many, “exponential growth” is synonymous with “really fast...
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Simulating Rule 110 in Opus Magnum
In my previous posts about the 2022 Opus Magnum tournament, I mostly left out the final puzzle. It deserves a post of its own. The puzzle concept shares ideas with the “making a computer” puzzle, so...
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Using Opus Magnum computers.. irrationally
This is going to be a short post about a design from a few months ago. Because the 2022 Opus Magnum tournament was still ongoing, I didn’t do much writing during those months. It began with a...
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Solving Freudenthal’s Impossible Problem
Alice declares “I am thinking of two whole numbers between 3 and 100. I have told their sum to Sam, and their product to Polly.” Sam says to Polly “You don’t know the numbers.” Polly replies “That was...
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Building arbitrary Life patterns in 15 gliders
The Conway’s Game of Life community celebrated a landmark achievement on November 9th, 2022. An idea years in the making, the “Reverse Caber Tosser” design finally had all of the pieces it needed to...
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Matching Patterns using Opus Magnum
Hi all, and merry Christmas to those of you who celebrate it! Here’s a present from me, a long-awaited blog post about the computation puzzle from the 2023 Opus Magnum tournament. The previous post...
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Revisiting Number Theory and the Impossible Puzzle
A couple years ago I wrote about the impossible puzzle, also known as the “sum-and-product puzzle” or “Freudenthal’s Problem”. That post was also my entry for the Summer of Math Exposition, where I...
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