# Selection Camp

Hey look, a post!

Amidst the two times five days of math camp and all the accompanying extra schoolwork (plus midterms (plus compound interest produced by procrastination)), I haven’t been writing a lot. So this post has been accumulating for perhaps a month, and there are still a few interesting bits left out because they’re relevant to what might be the next post.

I could try to record everything that happened during the two camps of math immersion I’ve been going to in the last couple of weeks, but that would be boring to read and to write. The interesting bits simply aren’t common enough to justify all that. Still, I should at least write something about exactly what I skipped six days of school plus the normal midterm date, for everybody who is curious, because I do not know the cardinality of that set, er, how many people that is.

But first a completely irrelevant aside: I put “apmo problem release date” into Google and got my last text-based post as the fifth hit. I tried again in an incognito Chrome window to make sure Google wasn’t bubbling based on my account, and then through a random proxy in France just to be safe. What conclusion am I supposed to draw? Maybe, nobody is blogging about this stuff? A negative correlation between math competition and rambling indiscriminately online? No idea.

*drum roll*

A few words of warning: firstly since people don’t actually use English this is all loosely translated, a rather lossy process in terms of atmosphere. But I’m too lazy to write everything down in two languages, so this is all there is. Also, if you don’t know enough math then some of the humor will go right over your head. But the idea that there are significantly many readers of my blog in that category is probably just wishful thinking.

***

The APMO this year had five problems culminating in a rather difficult inequality (to say the least) with a random official solution nobody thought of. This turned out to produce some very interesting facts. People didn’t seem to want to discuss them during camp as much as I expected, given that the official problems hadn’t been released and discussing with anybody else was taboo. Nevertheless, it still entered the discussion.

Alumnus CLK verified that nearly everybody who had fully solved it, about four or five people in all, had entered the first stage; he had checked for this particularly. There was definitely at least one exception, though… some mysterious person whose score was 0,0,0,0,7, only getting this insurmountable problem and neither the trivial #1 nor the straightforward #2. (single-use joke courtesy WL: this guy is even better than 007! No, not a factorial sign.) I suck at inequalities so my judgment may not be the best here, but this is pretty freaking ridiculous.

To make things even weirder, somebody said that SCH, who is widely worshiped as a god of olympiad algebra and reportedly had met less than three such problems he couldn’t solve, didn’t get this problem either. So, on the spot in the first stage of camp, we called for everybody who solved it to raise their hand.

Aaaaaaaand not a single hand went up.

Somebody called “Kick out the Communists!” (A quick search shows that the Chinese phrase in question, although literally interpretable as such, is actually a very strange phonetic mangling of something like “Come out and say it!” Come to think of it, I don’t actually know which one that person intended, but the (politically-?)incorrect one is funnier.)

Even after camp 1 ended, 2 started, and we got to ask administratively-higher-level alumnus PYC, we still don’t know what happened.

Of course it didn’t end there; people were “interrogating” each other about the question for a good while, with conversations such as:

“Was it you?”

“Heck no, I didn’t write a single word!”

“Oh, amazing! A proof without words!”

“I left my solution blank for that problem too… what if they think we copied off each other?”

***

CLK scribbled two long, verbose algebra problems on the whiteboard. Downstage, everybody murmured about the possibility they came from the scary CMO. After a bit of time we destroyed the first one and stumbled through his explanation of the second. Afterwards:

“Which country do you think these came from?”

scribble: A. Turkey; B: Kazakhstan; C: Serbia; D: none of the above. People raised hands…

“Actually, I came up with them myself.” *weird college math diversion*

Apparently, this is how all the less-awesome problems come into existence.

***

First night of the second stage, after the first minitest, which was one super-trivial not-even-really-geometry and one what-do-you-mean-it’s-just-Cauchy-Schwarz triplet of summations. Roommate and I derped in room. I pulled out a scary CMO problem book. He asked, “Can I see that?”

A few instants later: “Woah, what the heck is this?”

On the cover were the exact same three summations, down to each of the subscripts and variable names, and I hadn’t noticed until he pointed it out. The only difference was one upper index being 5 and the other being $n > 5$. I spent the next ten minutes flipping through the book, and the ten minutes after that double-checking. It was not one of the problems inside.

Later on people would start finding problem after problem after problem on AoPS, including one posted in December 2010. Wait, so that wasn’t from the shortlist?

(Well, to be fair, a problem stronger than APMO #1 appeared on AoPS in 2005. But APMO #1 is trivial and many of the ones we found were solved by zero people, so this comparison is not really fair anyway.)

***

Emissary Crisis, a new board game! I can’t think of any good analogies, but the idea is people are spies with secret alignments and send each other messages, which can be helpful or harmful. Each of the roles gets weird abilities and every card has a cool message on the side or bottom.
“The blood of the weak, although impure, is still sweet.”
“War and gambling both require tokens to bet with.”
“Destroy everything…”

Random in-game events translated into English (which doesn’t preserve the spy-jargon coolness, in my humble opinion)
“I Delete that card!”
*A lays out card* “Counteract!”
which is basically a card that prevents your action card from being used
*B lays out card* “Counteract your Counteract!”
*C lays out card* “Counteract your Counteract of Counteract!”

Counteractception! Okay, I think it sounds pretty lame in text. Oh well.

***

Number Theory class.

I was a bit annoyed because most of the stuff was basic, never going beyond Euler-Fermat. But then the teacher got to the ending section about the Mersenne prime search and how his computer was testing one right now, which led right into the strange $\sqrt{3}$ fields or whatever that made me sadface.

“It’s a good idea to memorize powers of 2 up to, say, the 20th power or so.”

WRC: “I have them memorized to the 30th power!”

“And say, powers of 3, of 5, of 7… you should probably get to the fourth power of 7 for that… 11 isn’t that hard because it’s just Pascal’s triangle, et cetera…”

Somebody shouted, “Powers of 10!”* Trollololol.

The other cool bit was where he quickly demonstrated and explained that algorithm for calculating the day of the week, the Doomsday algorithm. “It’s useful for attracting chicks! Hey, you guys eliminated all of them!” (There was a bonus joke in Chinese wording.)

* (NOT A FACTORIAL SIGN)

***

In the style of r/nocontext, an “Original Problem”: Prove that a polygon with $n$ sides has less than $\sqrt{n}$ centers of symmetry.

***

GJC was nominally looking for people to chip in their night-snack budget. We got NT$30 every night to buy something (in fact a “food item”); they talked about something in the convenience store costing NT$210.

What huge would cost NT\$210? I took a look in the store.

Er.

Okay.

If you are an astute reader or read TVTropes a lot you can guess what kind of thing I’m talking about. Otherwise, too bad.

***

That’s all I have for now. Four days until a whole new set of random stories (which probably won’t get posted until four weeks later)! Seeya.