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Solving Fizz Buzz with Cosines

susam.net

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Re: Solving Fizz Buzz with Cosines

#11

Post by darth_aardvark »

stronglikedan wrote: post #9
arealaccount wrote: post #6

Earlier quoted context omitted.

This would be an offer on the spot from me

> me: It's more of a "I can't believe you're asking me that." > interviewer: Great, we find that candidates who can't get this right don't do well here. > me: ... Shit attitude from that candidate, considering the interviewer is completely correct. I wouldn't hire them since they are obviously a problem employee. For those that don't know, Fizz Buzz is less an aptitude test and more of an attitude test. That's why th…

For those that don't know even more, this interview never happened and this interviewer doesn't exist. It's a funny joke on the internet.

Re: Solving Fizz Buzz with Cosines

#12

Post by NitpickLawyer »

stronglikedan wrote: post #9
arealaccount wrote: post #6

Earlier quoted context omitted.

This would be an offer on the spot from me

> me: It's more of a "I can't believe you're asking me that." > interviewer: Great, we find that candidates who can't get this right don't do well here. > me: ... Shit attitude from that candidate, considering the interviewer is completely correct. I wouldn't hire them since they are obviously a problem employee. For those that don't know, Fizz Buzz is less an aptitude test and more of an attitude test. That's why th…

> Fizz Buzz is less an aptitude test and more of an attitude test

The amount of (highly credentialed) interviewees that can't 0-shot a correct and fully functional fizzbuzz is also way higher than a lot of people would think. That's where the attitude part also comes in.

Re: Solving Fizz Buzz with Cosines

#13

Post by nine_k »

Well, there must be an obvious solution where the fizzbuzz sequence is seen as a spectrum of two frequencies (1/3 and 1/5), and a Fourier transform gives us a periodic signal with peaks of one amplitude at fizz spots, another amplitude at buzz spots, and their sum at fizzbuzz spots. I mean. that would be approximately the same solution as the article offers, just through a more straightforward mechanism.

Re: Solving Fizz Buzz with Cosines

#14

Post by atemerev »

nine_k wrote: post #13

Well, there must be an obvious solution where the fizzbuzz sequence is seen as a spectrum of two frequencies (1/3 and 1/5), and a Fourier transform gives us a periodic signal with peaks of one amplitude at fizz spots, another amplitude at buzz spots, and their sum at fizzbuzz spots. I mean. that would be approximately the same solution as the article offers, just through a more straightforward mechanism.

Yes. Exactly. This is how it _should_ have been done.

Also probably easy enough to encode as quantum superpositions.

Re: Solving Fizz Buzz with Cosines

#15

Post by isoprophlex »

What a neat trick. I'm thinking you can abuse polynomials similarly. If the goal is to print the first, say, 100 elements, a 99-degree polynomial would do just fine :^)

EDIT: the llm gods do recreational mathematics as well. claude actually thinks it was able to come up with and verify a solution...

https://claude.ai/share/5664fb69-78cf-4723-94c9-7a381f947633

Re: Solving Fizz Buzz with Cosines

#16

Post by susam »

nine_k wrote: post #13

Well, there must be an obvious solution where the fizzbuzz sequence is seen as a spectrum of two frequencies (1/3 and 1/5), and a Fourier transform gives us a periodic signal with peaks of one amplitude at fizz spots, another amplitude at buzz spots, and their sum at fizzbuzz spots. I mean. that would be approximately the same solution as the article offers, just through a more straightforward mechanism.

That is precisely how I began writing this post. I thought I'd demonstrate how to apply the discrete Fourier transform (DFT) but to do so for each of the 15 coefficients turned out to be a lot of tedious work. That's when I began noticing shortcuts for calculating each coefficient c_k based on the divisibility properties of k. One shortcut led to another and this post is the end result. It turns out it was far less tedious (and more interesting as well) to use the shortcuts than to perform a full-blown DFT calculation for each coefficient.

Of course, we could calculate the DFT using a tool, and from there work out the coefficients for the cosine terms. For example, we could get the coefficients for the exponential form like this:

https://www.wolframalpha.com/input?i=Fourier%5B%7B3%2C+0%2C+...

And then convert them to the coefficients for the cosine form like this:

https://www.wolframalpha.com/input?i=%7B11%2F15%2C+2*0%2C+2*...

That's certainly one way to avoid the tedious work but I decided to use the shortcuts as the basis for my post because I found this approach more interesting. The straightforward DFT method is perfectly valid as well and it would make an interesting post by itself.

Re: Solving Fizz Buzz with Cosines

#19

Post by HPsquared »

atemerev wrote: post #14
nine_k wrote: post #13

Well, there must be an obvious solution where the fizzbuzz sequence is seen as a spectrum of two frequencies (1/3 and 1/5), and a Fourier transform gives us a periodic signal with peaks of one amplitude at fizz spots, another amplitude at buzz spots, and their sum at fizzbuzz spots. I mean. that would be approximately the same solution as the article offers, just through a more straightforward mechanism.

Yes. Exactly. This is how it _should_ have been done. Also probably easy enough to encode as quantum superpositions.

How would someone do FizzBuzz on a quantum computer? It seems like a nice toy example problem.
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