HN user
Right; see Lakatos. In its roughest form, you study the structure of whatever counterexamples you find, add those as (negated) preconditions to your proposition, rinse and repeat until you have a true statement. If the proposition remains useful, you now have a new definition.
In fact, you don't even need an LLM tournament when you can have tom7's Elo World tournament: https://www.youtube.com/watch?v=DpXy041BIlA
3b1b just started a series under this slogan. Only one episode so far but chances are it'll be a good one; https://www.3blue1brown.com/
There are ways to make it work, but it requires using it only supplementary and with strict discipline. And it will look different for a 6-year old than a 13-year old.
But think of this trick we use about turning a tricky research paper in maths/science into something more tangible by making an LLM whip up an interactive version. That works at every level of education, and it means that you can completely tailor a piece of educational material to the kid
Tiny example: one kid was introduced to fractions and found it abstract that it was both about partitioning stuff and about numbers on a number line. So while we were practicing, I had an LLM make https://fuglede.codeberg.page/broeklegeplads/ to make it more hands-on.
Obviously for the small kids, this has to be an experience guided by teachers and parents, but for bright older kids with sufficient discipline that ought to be a useful trick for enhancing education.
Of course when we were kids, we would just write such educational programs ourselves and get the same effect /and/ learn to program (before getting banned from the computer room for putting spooky /binaries/ on the computers anyway), so maybe that's better for older kids. And maybe these kids will never have to do any maths or programming because the AI overlords have taken over when they grow up.
I wouldn't be surprised if this was never acknowledged by Meta.
It will, at least, have to be acknowledged by making GDPR Art. 33 notifications.
I've reached for this solution many times too; it's certainly convenient.
What I don't like is that all the resulting pages look the same. It's so easy to tell when a page is authored by Claude, and by now, I get the same “ugh another one” feeling as Dall-E generated images would give when they were completely overdone.
Maybe it's just be, but if not, maybe HTML generated outputs will also end up being dialed down from where they're at now.
But maybe not, since it's obviously a useful thing to be able to do. I wonder if there's a way out. To be able to introduce some natural entropy so not everything ends up looking the same. I guess not, since we're using machines whose natural mode of behavior is regression toward the mean. And maybe having it be harder to tell the author wouldn't even be desirable anyway.
So they're changing the product that people already paid an annual subscription for to the worse. That's asking for legal complaints.
It would be very helpful to know in understanding the capabilities of the models; and in getting intuition about where they are best applicable.
If the reason it was able to output the proof is that it happened to be included in an in-house university report written in Georgian, then that would make it less useful for research than if it's new entirely.
The XOR swap trick also features in the compilation/synthesis of quantum algorithms, where the XOR instruction (in the form of a CNOT gate) is fundamental in many architectures, and where native swapping need not be available.
One extension that I ran into, and which I think forms a nice problem is the following:
Just like the XOR swap trick can be used to swap to variables (and let's just say that they're bools), it can be extended to implement any permutation of the variables: suppose that the permutation is written as a composition of n transpositions (i.e., swaps of pairs), and that is the minimal number of transpositions that let's you do that. Each transposition can be implemented by 3 XORs, by the XOR swap trick for pairs, and so the full permutation can be implemented by 3n XORs. Now here's the question: Is it possible to come up with a way of doing it with less than 3n, or can we find a permutation that has a shortcut through XOR-land (not allowing any other kinds of instructions)? In other words, is XOR-swapping XOR-optimal?
I'm not going to spoil it, but only last year a paper was published in the quantum information literature that contains an answer [0]. I ended up making a little game where you get to play around with XOR-optimizing not only permutations, but general linear reversible circuits. [1]
[0] https://link.springer.com/article/10.1007/s11128-025-04831-5
I've always loved this recording of Thurston talking about branched coverings and knot complements using big knots: https://www.youtube.com/watch?v=IKSrBt2kFD4
I forget; did he receive anything in turn for taking that name? These folks did: http://news.bbc.co.uk/2/hi/africa/6157612.stm
And for desktop apps, Cinny has custom emoji/sticker support. Would be nice if they played better with Element though.
Median salary for a dev is about $130,000 according to https://www.prosa.dk/raad-og-svar/loenstatistik-2025 (assumes 37 hour work week, 5 weeks of vacation).
https://www.transparency.org/en/cpi/2024 offers some methodologies.
Just to not feed the witch hunt further, note that human 30 second solve times can be entirely possible for the easiest puzzles, with enough experience, practice, and a bit of risk-taking; see e.g. https://adventofcode.com/2021/leaderboard/day/1 part 1. But the 4 second solution times we saw last year are not, no matter how you look at it.
There's some good discussion here: https://old.reddit.com/r/adventofcode/comments/1h9cub8/discu...
But yes, you would have people openly share repositories for automatically ingesting the puzzle text, solving the puzzles, and submitting the results the moment the puzzles opened, leading to inhuman solution times. So, despite the rules stating that you can't do that, the result is that whenever the puzzles were easy enough for an LLM to solve them with high probability – and most of them are – the leaderboards would be overrun with such solutions.
In 2023, the LLMs would still struggle enough that the overall leaderboard (taking all 25 ⋅ 2 puzzles into account) would still be dominated by ordinary people (many of them recording their solutions), in 2024 that was no longer the case. Personally I would go from being able to top 100 regularly, to almost never being able to. I'm going to miss the thrill, and think it's a bit saddening that we can't have nice things, but also ultimately think that getting rid of it is the best option.
The triakis tetrahedron fit really is crazy close: https://youtu.be/jDTPBdxmxKw
Hm, yeah, tested it down to about 500 px width, and the low-resolution devices in Chromium but that was too optimistic then. The modals should of course be closeable, and both game boards simultaneously visible. Played around with the modals a bit, so maybe it works better now?
Yeah, the problem is in a sense solved asymptotically by the optimal construction in https://arxiv.org/abs/quant-ph/0302002, but that one tends to lead to long solutions in practice, so there's plenty of room to try to come up with solutions that give shorter solutions for concrete instances.
That's nifty! There's a lot of symmetry that can help to boil it down. For example, you actually only need row moves, and any solution with column moves can canonically be turned into one with row moves; post-composing with Ci→j is pre-composing with Rj→i.
One can think of the set of all possible board configurations as the vertices as a graph, with edges indicating how to move between configurations. Then your 1536 solutions are the 1536 distinct shortest paths between the starting and target configuration.
Then, you can also choose to consider not just board configurations, but board configurations up to simultaneous permutation of rows and columns; that will also reduce the number of unique solutions.
Thanks for sharing your thoughts!
I know of some work on trying out various heuristics for A*; Section 5 of https://arxiv.org/pdf/2201.06508 gives some examples of what works and what doesn't. I don't think D* Lite specifically has ever featured. There's plenty of room for trying to come up with other heuristics, and just for other takes in general.
But for bigger boards you won't be able to materialize the whole graph.
If we restrict to boards corresponding to solvable puzzles, the number of vertices is https://oeis.org/A002884 (1, 1, 6, 168, 20160, 9999360, 20158709760, …) and indeed grows quickly. It's possible to manipulate the 7×7 case (https://arxiv.org/abs/2503.01467, shameless plug) but anything bigger than that seems hard.
One can ask, for example, how many moves are needed for the hardest n×n Swapple. For n = 1, …, 7 the answers are 0, 3, 6, 9, 12, 15, 18 respectively, but we don't know what the answer is for n = 8.
The confetti is currently there for when you find a shortest solution. I'd say 13 moves deserves at least a star or two, so I'll have to add that!
Heh, nice catch, I think you'll find that with a bit of work, you can make row reduction/Gaussian elimination work here as well. But that the resulting sequences of operations can get very long! One thing I personally like about the puzzle is that once you've played it for a few days, you start gaining some intuition about sequences of moves that are useful, but coming up with a good general algorithm (that also works for larger than 4x4 boards) is still a challenge.
Yep, I see what you're saying; let me try to clarify that part!
I have lived in several parts of Denmark and never once encountered the notion of "lørdagsslik"; that concept sounds completely absurd and laughable. No, in every place I have stayed, kids would only ever have fredagsslik (Friday goodies), to be consumed while watching FredagsTamTam (https://www.dr.dk/drtv/serie/fredagstamtam_357146).
(2018)
The point is that if you input, say, 00001, then you will have tested both 0000 and 0001.
How about qwant.com? Privacy friendly, no nonsense by default.