supernewton

Dan and Lisa's answers agree on all but problems 6 and 9, and Dan got two more correct than Lisa. So Dan is correct on both 6 and 9. Therefore, Mary is incorrect on 6 and 9. So she got seven of the other eight correct, and Dan got three of the other eight correct. But on those eight problems, Mary and Dan disagree on only problems 2, 3, 5, and 10, therefore Mary got all four of those correct. Then Mary got three of problems 1, 4, 7, 8 correct, but everyone answered the same way on those, so Colin got three right on those problems as well. Then read off the deduced answer key for the other six problems to get Colin's final score.

Your body actually produces a small amount of cyanide endogenously, if it makes you feel any better. It has some role in cell signalling.

Note that being able to do this would imply P=NP.

I feel like https://xkcd.com/221/ might be heavily influencing what the typical "random" die roll looks like on the internet ;)

The thing you're missing is that at no point is it assumed that there are exactly two elements in a boolean algebra. In fact you can have a boolean algebra with four elements (see https://en.wikipedia.org/wiki/Boolean_algebra_(structure)).

Wizards of the Coast's in-house card database (Gatherer) is basically not maintained at all. I think they're very happy there is a third party willing to do that for free, and for a game with as much history as Magic, having a searchable card database is basically mandatory.

It is not. a and b are not symmetric in this equation, you can't just swap them.

You know he's been responding directly on Scott Aaronson's blog, right?

This is covered by the article. A board game might take 4 people and 2 hours to play. If your three friends didn't have fun with a board game the first time, they probably won't want to play again, and so you won't be able to play again either. Therefore there is a strong drive among boardgamers to play the "full" game the first time, because there might not be a second time.

It also adds extra difficulty to design a game that even has a simple version that is fun to play. Take your Texas Hold'em example, imagine it takes 2 hours to play one game. If you start with a version that has all cards face-up and no betting, people would conclude that Texas Hold'em is a supremely boring game, and wouldn't bother to try the full Texas Hold'em experience!

An American's life expectancy when they're born is around 76. But the life expectancy among Americans that have already lived to the age of 65 is more like 83.

The conjecture is true for all small graphs that they tried, so if it's "obviously" false to you then something went wrong with your intuition somewhere.

The third sentence is "If the kid searched specifically for the video and found it, TikTok would have been safe."

For air transport in the U.S., it's not just one certificate, it's many. You get your private license, instrument rating, multi-engine rating, commercial certificate, instructor certificate, and finally the air transport certificate. And you're not allowed to even think about that last step until you've accumulated 1500 flight hours on the previous steps. Being allowed to write a Javascript login page is easy pickings compared to that.

Sure, but in practice there don't really seem to exist "natural" problems that are both in P and are worse than O(n^3) or so.

By "natural" I mean a problem that one would actually want to solve, not some contrived problem specifically to make it O(n^100) since that's obviously easily possible.

You don't get to have "hidden information". The code used to respond "yes" or "no" to the guess would be part of the problem input. But, we currently can't prove there doesn't exist some algorithm that can examine that code and figure out what the "yes" input is faster than brute forcing all inputs.

Ambiguous parses aren't even the worst of it -- the worst are the ones that require real world knowledge.

"I couldn't fit the trophy in my suitcase because it was too big."

"I couldn't fit the trophy in my suitcase because it was too small."

Similarly, Vatican City has slightly less than 6 popes per square mile.

Anecdotally, with practice, some people can flip a coin to a desired outcome like 65% of the time. And .65^20 is only around 1 in 10,000.

They're the feeder contests in the U.S. that determine who gets to represent the U.S. in the IMO.

AMC = multiple choice test, open to all grade school students.

AIME = open response test, all answers are numerical, open to students who score high enough on AMC only.

USAMO = USA Math Olympiad. IMO-style proof problems. Open only to top N scorers on AMC and AIME.

Laypeople use "exponential" to mean "superlinear". It's fine, probably.

The U.S. has legislation limiting consumer liability of credit card fraud to $50, and many cards will further waive that to $0. It's just simply not the consumer's problem if someone copies their credit card number and uses it for fraud. They just have to call the bank to report the fraud, and then the bank will cancel the old card, issue a new one, and then it's the bank's problem on how to get the money back.

There are obviously commonsense exceptions granted.

Also, you can fulfill the swim requirement by taking 1 beginner swim class regardless of whether you actually learn to swim during that class or not.

There's another problem, the original one that quantum computers were conceived to solve: Simulating a quantum system.

If a and b are the golden ratio and its conjugate, then f_n = a^n + b^n. But since |b| < 1, you can just do f_n = nearest_integer(a^n).

Well, almost. You need to multiply by a factor of 1/sqrt(5) before rounding.

20 or 30 years ago, there were pay phones everywhere. I might not have carried a phone in middle school, but I did carry quarters that I could use to call my parents if anything ever went seriously sideways.

It still turns transactional. Maybe the parent has a job that is usually flexible but they have to put out fires every now and then, they'd happily sign up for this deal. Meanwhile it solves none of the daycare's problems and only adds new ones.

You probably don't have any issues because your daughter is well behaved, but fingerprint auth is probably one of the easiest things for a child to defeat - just wait for the parent to fall asleep!

Somewhat silly example: given a plane in 3 dimensions defined by x+y+z=1, we have ∂x/∂y * ∂y/∂z * ∂z/∂x = -1.

Do you honestly think the only thing that's changed about life between now and the 70s is your house and TV are bigger?

Absolutely not. Unless you have a strong mathematical reason to expect it to show up, instances of the golden ratio is largely numerology bullshit.