OscarCunningham

The one they give also crosses numerous rivers and lakes. For the strict version of the challenge where you literally can't cross water it's likely that the best solution is across Antarctica. Guaranteed by temperature to contain no water whatsoever.

There's a longer land path that starts in or near Senegal and ends in China. But they miss it because it goes near the Dead Sea, and they treat anything below sea level as water.

It's also robust to errors in the mesh. Like if the triangles don't quite join up it still gives a reasonable answer. https://mathstodon.xyz/@keenancrane/109388206643166726

You could maybe determine this using a SAT solver. You would have to encode the entire QR code specification. I was thinking of doing this to find a minimalist QR code that just had as few black cells as possible.

By the same author: https://mathstodon.xyz/@andrewt/115056697540191327

I think you're in the wrong thread. This one is about Claude producing counterexamples. The Go thread is next door.

I wouldn't have expected that there was post training specifically on the issue of looking for proofs vs counter examples. But it might be that other post training has a side effect of making AIs better at looking for counter examples. I wonder if these agents are overall less biased and more rational than humans. Can you expand on what you mean by goal based training?

They're trained on human data. I would expect them to emulate human biases as closely as possible.

The AI understands context so it's able to spot typos even when they coincidentally make reel words.

One argument would be that Ozempic doesn't give your body any additional resources. It just triggers your body to behave in a different way. But if the changes it causes are universally good, why didn't evolution already make your body work that way?

I suppose the counterargument would be that modern life is different from the evolutionary environment, and so it's possible for a change to be beneficial now that wasn't beneficial then. But it would still be good to understand better the mechanism of the effect of Ozempic on things like addiction.

John D Cook gives more technical details here: "Trying to fit a logistic curve" https://www.johndcook.com/blog/2025/12/20/fit-logistic-curve...

I've been wondering if you could do a similar thing for a Droste effect image containing two copies of itself. Packs of Laughing Cow cheese show a cow with two earrings, each of which is a pack of the cheese.

Oh I get it, the onion is made of Swiss cheese.

It seems like a lot of the difficulty is in finding arrangements that satisfy constraints. I wonder if an alternative approach would be to use a SAT solver. I suppose the problem with that approach would be that the solver might always find an 'easy' solution that doesn't look random. I know that some SAT solvers let you randomly assign the initial assignments of the variables, but that doesn't mean you get a random solution. Has anyone tried a similar approach?

This is a deliberate choice by Congress to give the Fed a mandate to target 2% inflation. In particular Congress hasn't given them any instruction to try to make up for mistakes. If inflation overshoots in one year then they don't try to undershoot in the next year. They just keep trying to hit 2% inflation.

So if retailers tried to lower prices to pre-COVID levels then they would fail. The Fed would see the falling prices and cut rates until 2% inflation was achieved.

Does this mean that if Earth stays a fixed distance from the sun then its equilibrium temperature is fixed? I remember people saying things like that the albedo of the ice caps affected the Earth's temperature.

Is it known which algorithms produce 'difficult' mazes? I'm imagining you could run all the maze solving algorithms against all the maze generating algorithms many times, and then calculate what the Nash equilibrium would be if the solver is trying to minimise expected time and the generator is trying to maximise it.

Enclosing a settlement gets easier as it gets larger. The amount of work is proportional to the perimeter, while the number of people to do the work is proportional to the area. The area is proportional to the square of the perimeter, so the work per person is inversely proportional to the length of the wall.

Another example: ears are excellent at breaking down the frequency of sounds, but are imprecise about where the sound is coming from; whereas eyes are excellent at telling you where light is coming from, but imprecise about how its frequencies break down.

There's an old Flash game called 'Chat Noir' where you have to trap a cat on a hexagonal grid. Here's a copy of it: https://www.hoodamath.com/games/chatnoir.html

But is a geostationary satellite going around the Earth?

Right. Interesting small patterns can be found using clever search algorithms. There's also the approach of running trillions of random 'soups' and scanning the results for interesting patterns. These small patterns are then pieced together to build the larger structures.

The problem is when you bisect an odd sized group. You necessarily have to make one half larger than the other. So you're not trying to misdirect, you're trying to avoid creating a signal. But to do this you have to sometimes put your character in the smaller half, which trades off against your other goal of shrinking the pool as fast as possible.

One thing this doesn't take into account (and the paper acknowledges this) is that the characters are assigned by picking cards from a deck. So the two players cannot have the same character.

Taking this into account would make the game much more complicated, because it can introduce an element of bluff.

For a simple example, imagine that there are only 5 characters. On your first turn you know the opponent doesn't have the same card as you, so you've got 4 options remaining. You'd like to ask a question that splits them into 2+2, but if you do this then the card you're holding will make one of the groups into a 3. Your opponent will know that your card is one of the 3, so you've effectively given them a head start. Instead you might sometimes want to split the options 3+2 with your card in the 2, as a bluff.

How often you want to do this must be described by some Nash equilibrium probabilities. It would be interesting to set up a linear programming solver to find these exactly, but so far I haven't had time to set this up. I don't know if it would be practical to solve the full version of the game with 24 characters.

Fans of Celtic knots might also like the daily game Celtix (https://www.andrewt.net/puzzles/celtix/) where the objective is to separate a Celtic knot into five coloured strands.

I've even seen the BigQuery formatter change the behaviour of a query, by mixing a keyword from a comment into the real code.

The issue that spawned scalping and Ticketmaster is that musicians want to sell tickets under their market value. There's no analogous issue with airline pricing.

I had the opposite problem at my last company. When you hover over a link Apple's Mail app opens a preview of the page. So if you try to see the URL then you automatically visit the link and get sent for more training.