Seven on an asteroid – a mathematical puzzle

I happened to see this puzzle on Facebook. Really nice puzzle (if rather hard).

Seven astronauts are exploring a small spherical asteroid. All seven started out in the same point.

Astronaut A went 30 kilometers in one direction, then turned 90 degrees to the left, then moved another 30 kilometers, then turned 90 degrees to the left again, and then moved for 30 kilometers more.

Astronaut B moved in the same pattern, except his movements between the 90 degree turns were 40 kilometers long instead of 30.

Astronauts C, D, E, F and G also moved in the same pattern, but went in sections of 50, 60, 70, 80, and 90 kilometers, respectively.

The astronauts started moving (from the same starting point) in several different directions, but, as it happened, after the movements described above, all but one ended up in the same place.

  1. Which astronaut ended up in a different place?
  2. How large is the asteroid?

Answers in comments (if there somehow are any).

(Post 172 in the inner system, incidentally. Post 4 in reality.)


On a recent political StackExchange question

Now that I actually have a blog, I might as well talk about something serious on it.
(I hate politics, incidentally.)

A few hours ago, I happened to see a question on StackExchange that reminded me of a similar issue I had myself.

The question is over here, and is basically asking why are there so many Trump voters when the question asker doesn’t know any.

The accepted answer gives the following summary:

All that can probably be summed up by saying:

  1. You aren’t finding Trump voters in your circles because you’re talking to college-educated people who were already interested in politics.
  2. Trump is winning because the voters in your demographic are splitting their votes among non-Trump candidates.

That’s not very significant to me at face value, because I didn’t even know Trump was winning anything until I saw the question, but it reminded me that until recently I wondered the exact same thing about Putin.

(Wait – the non-Russian readers here might ask, if I had any – Putin? Vladimir Putin? Totalitarian dictator of Russia? That Putin?
Yes, that’s the guy.)

In any case, Putin had been consistently polling at 55-75 percent (sometimes higher, sometimes lower, but nearly always within that range). Yet until fairly recently I knew pretty much nobody who would admit to voting for him, or to liking him for that matter (there was one guy who did; he also said that he wanted to join the army).

Then it was all explained to me: the sort of people who are interested in politics, or indeed the sort of people who are well-educated (which also happens to include most of the people I know and talk with), do, in fact, mostly vote for someone other than Putin (when they bother to vote at all, as opposed to spoiling their ballot as a protest). However, everyone else – the working class, so to say – seriously think Putin is their guy.

It didn’t help that the alternative candidates were a self-declared communist, a ludicrous conservative, and the occasional extreme dark horse (like Bogdanov). When there was a clear non-Putin liberal candidate (like Prokhorov), people did vote for them a lot (sometimes enough for them to get second place).


This changed a bit, lately, due to the Crimea thing.

Pretty much no one in their right mind, other than the occasional major contrarian (not that I have anything against contrarians – they can have their own opinions, it’s just that those opinions often sound silly), wants to admit that they actually want to give Crimea back to the Ukrainians – at least, not to their current government (and I suspect that even some of those who do say such things still do want to keep it, but happen to also think that keeping it is wrong for other reasons).

For that matter, it was a popular opinion (in Russia) even prior to 2014 that giving Crimea to the Ukrainians originally (back in the 1950s) was a mistake in the first place (an opinion that I happened to share).

However, it also happens that Putin’s opinion is that Crimea should be kept, and most of the West’s opinion is that Crimea should be given back (to the current Ukrainian government, by which I mean that of Poroshenko). So anyone whose opinion is that Crimea should be kept, and shouldn’t be given back to Poroshenko’s government (which is most Russians, including many that are otherwise anti-Putin) happens to agree with Putin on this point, and disagree with the West. Which kind of makes things hard for anti-Putinites (because they’re always pointed into the Crimean question).

I… really don’t know what to do there. Do the Western governments realize that by their continued insistence on return of Crimea, they’re only strengthening Putin’s position as a totalitarian dictator? (Which he might or might not actually be – depending on your opinions and especially definitions – but definitely is from those same Westerners’ perspective.) Does anyone in the West actually seriously think that Crimea would be returned to Poroshenko’s government? (If so, why?)
For that matter, if eventually the Poroshenko government itself is overthrown in another coup, will the Western opinion involve handing out Crimea to the new government, restoration of Poroshenko, or neither? If the second, this will be unpopular with both Ukraine and Russia; but so far such a scenario seems the most likely.


…Did I mention that I hate politics?
(This is post 64 in the inner system, incidentally. Also, the visual editor sucks, and I don’t know how to make the quote text smaller.)

My upcoming projects

My main upcoming project on this blog is Language Log Twelve Years Later – a witty commentary (oh, that’s where sarcasm comes in! I wondered why I thought it’s so likely to appear) on classic Language Log (the 2003-08 run, in theory, though I doubt it would get all the way there, and if it does I doubt it would stop at the boundary).
And by this, I mean there will be a commentary on every single article. Since very early articles were far away in time from each other, the gap will probably shrink for a while, but it would inevitably start to grow very quickly as articles become more frequent (up to several per day, and at times perhaps more). I do not intend to ever let it shrink to under 12 years (thus the title), but it would require much more frequent posting that I’m likely to produce anyway.

There are… 5500 or so classic Language Log articles, apparently. There are roughly 1700 days in its run, so that’s an average of 3.2 articles per day. (A bit more if we discount the slow start in 2003.)

…I’m pretty sure that’s not my only current upcoming project, but I really wanted to post this before the end of the 29th of February. I might edit this to add some more later.

(Incidentally, in the inner editing system, this is apparently post number 37. Even though it’s only my second WordPress post ever.)

I finally made a blog

Today is the first anniversary of the day when I registered on Coin Community.

Today is the third anniversary of the day when I translated my first limerick.

(Sadly I cannot recall anything I was doing on the day of which today would have been the second anniversary.)

Today is the fifth Monday of February; it is the first such day in my life, and the last combination of this type for which I can ever say that. As long as our calendar doesn’t change significantly, anyway.
(Though, to be fair, while the following fifth Saturday of February would be my second, during my first I was barely a baby.)

And today is the day when I finally started a blog. Aside from my LJ, anyway.

(I’m actually surprised that this name was still available. A bit less than I could have been, though, because I also checked a dozen or so similar simple names which were, in fact, taken already.)

The tagline is a deliberate reference to XKCD, incidentally.
(I do intend to write much about language and math, and probably some sarcasm if it ever comes up, but romance is indeed unlikely.)