[HN Gopher] Solving Fizz Buzz with Cosines
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Solving Fizz Buzz with Cosines
Author : hprotagonist
Score : 96 points
Date : 2025-11-21 17:28 UTC (5 hours ago)
(HTM) web link (susam.net)
(TXT) w3m dump (susam.net)
| thomasjudge wrote:
| https://joelgrus.com/2016/05/23/fizz-buzz-in-tensorflow/
| arealaccount wrote:
| This would be an offer on the spot from me
| stronglikedan wrote:
| > 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 this candidate
| failed and didn't get the job.
| darth_aardvark wrote:
| 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.
| NitpickLawyer wrote:
| > 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.
| n4r9 wrote:
| A massively over-engineered, incorrect solution?
| jiveturkey wrote:
| A candidate that appreciates the value of the question, yet
| won't subject themselves to the absurdity of demonstrating
| compliance.
|
| Yes, very much yes.
| gregsadetsky wrote:
| There was another great satirical take on FizzBuzz which had
| something to do with runes and incantation and magical
| spells...? I sort of remember that the same author maybe even
| wrote a follow up? to this extremely experienced developer
| solving FizzBuzz in the most arcane way possible.
|
| Does this ring a bell for anyone?
|
| ---
|
| Found it!
|
| https://aphyr.com/posts/340-reversing-the-technical-intervie...
|
| https://aphyr.com/posts/341-hexing-the-technical-interview
|
| https://aphyr.com/posts/342-typing-the-technical-interview
|
| https://aphyr.com/posts/353-rewriting-the-technical-intervie...
| (the FizzBuzz one)
|
| https://aphyr.com/posts/354-unifying-the-technical-interview
|
| wow.
| ntonozzi wrote:
| One of my favorite blog posts of all time:
| https://aphyr.com/posts/342-typing-the-technical-interview
| taolson wrote:
| Along that line, an over-engineered fizzBuzz using lazy list
| operations:
|
| https://github.com/taolson/Admiran/blob/main/examples/fizzBu...
| ivan_ah wrote:
| This is very nice.
| tantalor wrote:
| There are several mentions of "closed-form expression" without
| precisely defining what that means, only "finite combinations of
| basic operations".
|
| TFA implies that branches (if statements and piecewise
| statements) are not allowed, but I don't see why not. Seems like
| a basic operation to me.
|
| Nevermind that `s[i]` is essentially a piecewise statement.
| susam wrote:
| > There are several mentions of "closed-form expression"
| without precisely defining what that means, only "finite
| combinations of basic operations".
|
| There is no universal definition of 'closed-form expression'.
| But there are some basic operations and functions that are
| broadly accepted, and they are spelled out directly after the
| 'finite combinations' phrase you quoted from the post. Quoting
| the remainder of that sentence here:
|
| _' [...] finite combinations of basic operations such as
| addition, subtraction, multiplication, division, integer
| exponents and roots with integer index as well as functions
| such as exponentials, logarithms and trigonometric functions.'_
| siegelzero wrote:
| Very cool! There's definitely some similarity to Ramanujan Sums,
| though the approach here sort of packages the fizz-buzz
| divisibility properties into one function.
| https://en.wikipedia.org/wiki/Ramanujan%27s_sum
| layer8 wrote:
| I think that implementation will break down around 2^50 or so.
| nine_k wrote:
| 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.
| atemerev wrote:
| Yes. Exactly. This is how it _should_ have been done.
|
| Also probably easy enough to encode as quantum superpositions.
| HPsquared wrote:
| How would someone do FizzBuzz on a quantum computer? It seems
| like a nice toy example problem.
| susam wrote:
| 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.
| mr_wiglaf wrote:
| Ah so taking the Fourier transform of this function[0]? The
| summation of the fizz and buzz frequencies don't lead to
| perfect peaks for the fizz and buzz locations. I need to
| revisit Fourier cause I would have thought the transform would
| have just recovered the two fizz and buzz peaks not the
| fizzbuzz spot.
|
| [0]: https://www.desmos.com/calculator/wgr3zvhazp
| isoprophlex wrote:
| 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
| ok123456 wrote:
| I once had a coworker who used the FFT to determine whether
| coordinates formed a regular 2D grid. It didn't really work
| because of the interior points.
| throwaway81523 wrote:
| Where the madness leads:
| https://cspages.ucalgary.ca/~robin/class/449/Evolution.htm
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