setter: noun. One who does set theory.
What do new Sudoku techniques teach us about real-world problem solving?
41–50 of 71 posts
Re: What do new Sudoku techniques teach us about real-world problem solving?
#42Cracking the Cryptic (the Youtube channel mentioned in the article) is a great channel to follow. Especially Simon's videos offer great insight into his thought process solving through some pretty hard sudokus (and variants). They've also taken on different puzzle games (e.g. The Witness, Baba is You), and it's absolutely fascinating to see how being very highly skilled in solving one type of puzzle does or does not translate into other classes of puzzle.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#43Phistomefel’s Theorem (and the more general "set equivalence theory" described in the article) pops out directly from a standard technique known as the "Linear Programming relaxation" for Sudoku. Essentially, the Linear Programming relaxation of a puzzle is a standard way of approximating the solution space with a system of linear equations and inequalities, replacing discrete yes/no answers to questions like "is the…
Do you know any sources on on how set equivalence theory is related to integer programming? Because I don't see the immediate connection and I could not find anything on the internet, but maybe I used the wrong terms.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#44For anyone following along the article, it should be "Row 4, Row 7, Box 4, and Box 6" where it says "Row 4, Row 7, Box 4, and Box 7". Somebody please correct me if I'm misunderstanding.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#45For anyone following along the article, it should be "Row 4, Row 7, Box 4, and Box 6" where it says "Row 4, Row 7, Box 4, and Box 7". Somebody please correct me if I'm misunderstanding.
You are quite right, it's a typo in the article.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#46Earlier quoted context omitted.
3Blue1Brown has a few videos where he discusses and uses this technique to solve some complex problems. One of those was for a mathematical competition. It's also common in audio manipulation, e.g. change to the frequency domain in order to modify pitch, then change back to the time domain.
> It's also common in audio manipulation, e.g. change to the frequency domain in order to modify pitch, then change back to the time domain. Funnily enough, yes but actually no. For understanding and mathematical proofs the Fourier Transform is obviously essential. But when you first get into audio DSP programming it might seem that the FFT is crucial as well. But virtually all digital audio filters directly operate…
Is there any scenario where the discrepancy between FFT and its analog cousin cannot be resolved by upping the sampling density? Distortion is always there, whether it comes from an imprecise sensor/instrument or from extrapolating sampled data. In the audio space, nothing above 20 kHz is audible anyways, so even a bog-standard 44.1 kHz sampling rate should do "good enough" for most DSP operations there.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#47I don’t even care what the “real-world” implications are; this is just an awesome way to think about Sudoku, and number sets.
Re: What do new Sudoku techniques teach us about real-world problem solving?
#48Re: What do new Sudoku techniques teach us about real-world problem solving?
#49If I'm not mistaken, you can in fact get the same digit three times in the ostrich head.
EDIT: I misread the article — it said you can't place the same digit more than three times.
Such a deep dive on ontological remodeling that I found myself starved for oxygen about the time palindromic lines came up.
Phistomofel’s Theorem though blew my mind. I'm still trying to convince myself it is legit. (Probably where I started to think about heading back to the surface.)
Re: What do new Sudoku techniques teach us about real-world problem solving?
#50"Ontological remodeling" is a lovely term. I think it's ubiquitous actually, but another nice example is the puzzle about tiling a chessboard with dominoes when the board is missing two opposite corners. Can you do it? If so, how? If not, why not? Btw is the footnote a joke? I don't really get it: The sum of the digits 1 to 9 is 45[1] [1] This is a secret that Simon only tells his closest friends.
Also, using a similar trick as with the dominoes, can a certain Legend of Zelda puzzle be solved? https://gazj.substack.com/p/python-and-the-legend-of-zelda?s... Article doesn't contain a mathematical proof (only a brute force one), but I wrote one up. Spoilers: https://news.ycombinator.com/item?id=30639211
That's a cool puzzle! It's the same as the Bridges of Königsberg, right? If each square is a node, connected by edges to adjacent squares, then it's only solvable if there are at most two squares with an odd number of edges. Think about it like this: except for the squares where you start and finish, you must use one edge to enter and another to leave.
I guess the Zelda puzzle is different because in Königsberg you can revisit islands, just not recross bridges. But that feels like something you can finesse somehow. . . . Ah, just swap nodes & edges, right? Squares : bridges :: sides : islands. Indeed, that lines up not just the restriction but the goal too.
EDIT: Oh your second link is a much nicer solution. But still it feels like there is a relationship to Königsberg.