leah blogs: November 2023

26nov2023 · On division by three

I drafted this article in Feburary for a blog project that never came to realization, but as it’s a nice little article so I’ll just post it here:

I was thoroughly nerdsniped by a recent post on The Unix Heritage Society mailing list, where this anecdote was mentioned by Noel Chiappa:

Steve Ward told another oral story which I’m pretty sure is true, though. They ask the candidate to design a state machine (or digital logic, I forget which) which can tell if a number is divisible by three (I think I have the details correct, but I’m not absolutely certain). So they describe one – and then point out that you can feed the number in from either end (most or least significant end first) – and proves that it will work either way! The committee was blown away.

Since this sounded like an interesting statement, I tried to find a proof myself and found two solutions, one using automata theory and one using ordinary math.

Read as a PDF: On division by three.

NP: Lightning Bolt—No Rest for the Obsessed

Copyright © 2004–2022