I think that's a common misunderstanding about who owns what in a marriage. I'll quote Matt Levine on this:
One thing that I find a little weird about the Bezos divorce is that there are a lot of claims that it will make MacKenzie Bezos “the world’s richest woman.” I suppose there is a technical sense in which that is right, but it assumes not only that she will have a right to half of Jeff Bezos’s assets in divorce, but also that she has no such right in marriage. That strikes me as a strange way to think about marriage, and about the “community property” laws that might give her half the assets in divorce. (Surely those laws imply that she is in a sense a joint owner now?) I would have thought the more straightforward analysis is that she is the world’s richest woman now, because she is a member of a married couple that has more money than any other single person or married couple on the planet, but I guess that is not how the scorekeeping works.
In Haifa (Israel) there was a staircase race a few years ago, from sea level to the top of the city going up more than 1000 stairs. One version of this was doing it over and over so that the total is the height of the Everest. I'm pretty sure there were several runners who finished that successfully.
All the other answers in the thread focus on maximizing head-to-head score. I'll try to answer the question for the goal of greedily maximizing your own score.
Using the same definitions from the article, we now have (for a 2 person game):
Q_i = -P_i + (1 - sum_{j=1..i}(P_j))
Where the first term is for the case of choosing the same number as your opponent, and the second when it's larger than your opponent.
Now solve the same set of equations, but with our new Q_i. Solving Q_1 = Q_2 analytically is easy, then Q_2 = Q_3 and so on... You get P = (1/2, 1/4, 1/8, ...)
So that's the result for this specific 2-player game. You could also ask about the 2-player game with tie=t for any negative t (the above is for t=-1). Now we get
Q_i = t*P_i + (1 - sum(P_j))
Again, solving Q_i=Q_{i+1} is easy and gives
P_{i+1} = (t / (t-1)) * P_i
For example, if t=-2 then (using the fact that all P_i's sum to 1): P = (1/3, 2/9, 3/27, ...)
I did not try to tackle the 3-player game with tie=t.
The path with that label is blocked unless the condition is fulfilled. I don't think it relies on any prior knowledge (at least nothing specific I can think of)
On the contrary, it should be on by default for every build configuration! If you move to a newer compiler version and the compilation breaks, then you just saved yourself valuable debugging time. The alternative is that the new compiler has a new optimization that causes your code to break in runtime. You can always disable specific warnings if you think they're not relevant for your code.
There are some exit clauses (like Musk not getting financing from his banks) but they don't apply here. Specifically, there's no exit clause for the bot percentage.
> If it was a promise it could be written on a hallmark card.
Are you just trying to change the meaning of the word promise? Most people would agree that if you break a promise you pay a price - it might be a social one in case of a promise between friends. Or it might be a financial price in case of a written & signed promise, a.k.a a contract.
> Breastfed children tend to have less stomachaches.
Maybe on average, but specific cases can vary wildly. Some foods that the breastfeeding mother consumes can cause issues. Milk, soy, and caffeine are known troublemakers - but good luck finding out which one is the source of stomach issues for your baby!
Follow-up question: what if other countries follow suit, especially ones that don't use a Latin-based alphabet? Egypt is formally called "جمهورية مصر العربية" in its native language - should that be recorded as the ISO Full name for EG?
Same here. In fact I lost my 1000+ day streak 2 months ago (a newborn will do that to you) and haven't done a single Duolingo lesson since then. However, I did replace it with another app called DuoCards (no relation to Duolingo, AFAICT) which is great for memorizing vocabulary using spaced repetition. Duolingo used to have a companion app that did something similar, but they closed it a year ago. Anyway, they lost my subscription.
There's a link in the article to a paper (N2023) proving this is not constant time. The issue is that as you delete elements, and the hash table becomes sparse, finding the next nonempty bucket is not so fast. However, I believe that the paper conveniently glosses over the fact that there will be rehashing into a smaller table which would fix this issue.
This can happen anywhere, not only on software. I once bought a set of 10 or so entries to a climbing wall. Some time later I wanted to use it and was told that it was no longer valid. There was no "valid by" date on the card, but I was told that the place transfered ownership and that this decision to not accept the old card was ok'ed by the lawyers.
At least for software you can keep a copy of the installer. Unless it checks the license with the server, then you're screwed...
http://tom7.org/zelda/