Today we get away from the word games for a little while and get back to talking about random number generators (previous posts here and here). Or rather one random number generator in specific: a Rule 30 psuedo-random number generator (PRNG). (Here’s the motivating post from Programming Praxis.)
Remember the previous post I made about cellular automaton? The basic idea is to turn those into a random number generator. If you go back to the linked post in particular and give it Rule 30 with a random initial state, you can see how chaotic the rows seem to be. Perfect for a PRNG.
One more challenge from Programming Praxis’ Word Games today (there are only a few left!). This time we have the challenge of cutting off bits of words, one letter at a time, such that each step is still a word.
The example given in their post is planet → plane → plan → pan → an → a, although surely many such examples exist.
Continuing in my recent set of word-cube source code. Like yesterday, it’s designed to work in Racket 5.3+.
Okay, this one was just neat. Based on word-squares source. I’ve only tested it in Racket 5.3+, but newer versions should work as well. Racket 5.2 won’t work without some tweaking as (at the very least) it’s missing a definition for string-trim.
For the next few posts, we’re going to need a way to represent a dictionary. You could go with just a flat list containing all of the words in the dictionary, but the runtime doesn’t seem optimal. Instead, we want a data structure that lets you easily get all possible words that start with a given prefix. We want a trie.
Another day, another post from Programming Praxis. Today they posted a word game that seems simple enough: first find all words in a given dictionary that contain all five vowels (a, e, i, o, u) in ascending order and then find any words (at least six letters long) where the letters are all in ascending alphabetical order.
There’s been a bit of hubbub in the in the math world the last few weeks with Shinichi Mochizuki's 500 page proof that of the ABC conjecture. Basically, the conjecture states that given three positive coprime integers a, b, and c such that a + b = c, the product of the distinct prime factors of a, b, and c is rarely much smaller than c. While this may sound strange, there are a number of interesting consequences that you can read about here.
To make a long story shorter, there was a challenge on Programming Praxis that intrigued me, which was to write code that given a upper bound on c would generate a list of all of the triples (a, b, c) such that the product is larger.