Archive for April, 2012


of the post variety.


It’s a subtle one, but it exists. Mostly occured from a rather “coincidental” observation from somebody when this blog was 3 posts long. So I decided to “retcon” (probably misusing the word here) my posting schedule to fit this one. Some of you already know about this, but to those of you who don’t, I’ll just say that a) it leads to somewhat long posting breaks and b) I can’t just publish whenever I feel like it.


Also, while I do queue up posts, my queue of completed posts is stunningly small (read: queue size = 0). I do have half-complete posts though. As of last count, four.


This post will be fairly short, because I need to finish typing this post in around 3 minutes. Now 2 minutes. Also, I guess the previous post was unjustifiably long, and way too personal and nobody should care about that stuff. Although I suppose this post is as well. (although not “unjustifiably long”. Unjustifiably short?)


I don’t have any of it. Either physical or mental, as I have basically concluded.

So today was the Berkeley Math Tournament. Here’s approximately what happened:

BART @ 7:30: Load BART ticket, look semi-awkward waiting alone for rest of team. Overhear some person arguing with the station employees (what is there to argue over anyway?), meet up with some of the team. Surprise! Some of the team members that we regrettably either “kicked out” or volunteered away due to space issues defected to other teams. Funnily enough, one of these members (Kr.Bh.) was kicked out on the grounds of lack of school loyalty during a previous math tournament, SMT. Oops. So anyways, meet up with them, board bus (fine, train) initiate cardplaying. Teach someone how to play Napoleon (and you should too here: LINK. Warning: seizure alert, sorry if your eyes get blinded. Oh, and it’s pretty long. You might want to skip over the rules for Prime Minister (a Presidents variation) but that’s a pretty fun card game (at least to our mathematical clique) so yeah. We’re (well I can’t actually speak for our group but this is my opinion) open to people who want to play cards with us… as long as you somewhat know what you’re doing. Different people seem to have different thresholds of this “knowing what you’re doing” quantity though.) We later on transition to BS poker because it’s easier to play on a train, with not as much card-throwing. No, a high card does not beat a pair.

Berkeley @ 8:40: Walk out BART station. Al.Xu. insists that we go one way, but RH.Wu. and the rest of us go to other way. Apparently Al.Xu.’s way involves an escalator, and ours involves stairs. Exercise! After much undue “paranoia” about cars running over us (so it was a very good position to stay in the center, lest some erratic car comes hurtling through the directed roads in the wrong direction, although I do suppose that if that happened we were all screwed no matter what our relative position, especially if we’re on the sidewalk) we reach the auditorium. Hmm. Life sciences for a math tournament. Ah well. Play more Napoleon (teaching He.Ma.) and thus Napoleon is gaining ground in the math community. Yay. (We managed to make Prime Minister the SFBA exclusive card game the year before, and Idiot the year before that. (Mao and Uno precede this, although neither are very SFBA-exclusive or math-exclusive. Although I suppose you could make the same argument for Napoleon.) Both instructions in the link above.) Late double breakfast: acquire orange juice (but importantly, the plastic cup!) Plastic cups are not biodegradable, and thus do not taste very good. I do not manage to actually eat it, just rip it up into shreds. Oh well. Team registration occurs, and the Berkeley people are apparently more receptive on esoteric team name selection than the Stanford people. (We sent “·” (U+00B7, Alt+183) for Stanford, and “☺” (U+263A, Alt+1?) for Berkeley. The Stanford people, to put it simply, were not very amused, and casted the name to “.”. Darn.) So anyways, we get t-shirts, nametags, the general stuff. Back to cardplaying.

Power @ 10:20: Yay combo power. Darn why did I pick extremely bashy stuff. Induction lemma, induction proof that uses induction lemma. Too much work for only 7 out of 90 points! Then write up 4 pages rigorizing something for 8 points. What time’s up already? Ok let’s just say that it’s equivalent to what we want to show, and get it over with. Not the best performance, but considering we basically dropped about 30 points already of unsolved problems (No, Je.Wu., #12 was not solved), 15/60 is pretty good, considering how freaking long each problem took. My hand hurts 😦

Expected contribution: 15 max, perhaps -2 for that other problem.

Team @ 11:30: Tried #10, give up too hard. Tried #9, give up too hard. Doesn’t look good so far. Ohey #8 is trivial. #7 is trivial. #6 is trivial. #2 is trivial and why did our team not get this earlier. #5 is a pretty quick mem, for a confirm. Oh, and relook at number #9, gee the calculation looks kinda bad, but YES WE GET IT IN THE LAST FEW SECONDS!

Oh huh so apparently I misread #6 😦 Consolation points for solving their intended question? Darn. That diagram was totally not symmetric.

Expected contribution: …36 what? (half a question for #5, #9 I suppose – calculation was partially outsourced to Pa.Ze.) This is out of the 8 correct = 72 points. (we did not get #10, and 42 was unfortunately not the right answer – though it was actually a semi-legitimate guess!)

Too much carry. Two good rounds in a row is a recipe for disaster. I haven’t been able to consistently operate throughout a full-day math tournament (including SMT in the year which I topped both subjects AT/geo; I basically slacked on team/power that year) so this looks like a bad sign. Also, I necessarily have to take significant ~30 minute breaks on the USAMO and other similar olympiad tests, or else really bad stuff happens, like when I basically space out during MOP test #2, getting 8/28. Oops.

(That 30-minute break thing doesn’t really work for these short sub-hour rounds.)

Indivs @ 12:20: Blast through first six questions. #7 takes some time, #8 takes even more time (1/3 of the test?). Then #10 was a pretty quick observation, and #9 I got a few cases but not very much else.

In theory.

As it turns out, I miss one problem for thinking that 47 is divisible by 3, one problem for disregarding the fact that 34 and 70 are not relatively prime, problem #9 for not seeing that a particular case was trivially winnable, and one problem for misinterpreting the wording of the problem majorly. gg

Ouch, that hurt. 6 => 12 contribution points there. 😦


So, that’s around 13+36+12=61 points out of a maximum of 300, so yep I’ve basically done my share and overdone by quite a bit. But at a cost of a pretty terrible individual round. Which is interesting in a team perspective:

Getting one team question correct is basically worth about four and a half questions correct. This is what completely roflstomped the SFBA A1 ARML team last year: the team round. (Their proportion is actually higher, rated at one team question per 5 individual questions) We got like 6/10. And that is bad – compared to most teams who got 8/10 or even better, that would be akin to throwing away one individual perfect score :O. Mediocre power round doesn’t help either, but I suppose there wasn’t too much improvement to be made there (Oh, and apparently there were some grading issues that caused us to get no points on #3? I don’t know). But anyways, the team round really really failed for us. I don’t think coordination was the big problem actually; we did satisfactorily well on the power round. My theory? We just get tired. Ok, maybe not “we” but at least I feel pretty worn out after going through the power round.  And thus don’t rely on me to get 8, 9, and 10 all at once, because that’s not how I roll usually.


Lunch @ 1:30: But no, that’s not the end of the tournament. Afterwards there was lunch. After another slight “snafu” where we only get  four bags of burgers, instead of five… and two of the bags don’t even have fries in them (Don’t get me started on the lack of ketchup on any of them), we finish them. The burgers were pretty good – they’re probably more worth it than McDonald’s burgers, although you still cannot beat Burger King onion rings, hah. (I have a feeling that my taste of taste is weird) For price comparisons, that cost us $6, fries (at least it should have) and drinks included. Eventually we get two more boxes of fries, and all is good. I’m actually unsure of how much a McDonald’s meal costs, but I’d hazard a guess of around $6 as well if you’re not going ultra-cheap. Seriously, these burgers were actually pretty decent. Especially the bread.

But anyways some people felt that the $6 cost wasn’t worth it, so they got their meal via other means, such as going out to downtown Berkeley and buying food elsewhere. Somebody got a sandwich, and that comes with forks and knives. Also, I think Berkeley is generally considered a greenish community, so of course these forks and knives were special – they’re BIODEGRADABLE! And biodegradable clearly equates to edible right? By the way, sanitation is not a problem as that knife was not previously used.

So I got a knife. Don’t worry, I was semi-bored and not actually hungry. At first I try using canines to etch out of the flat part of the knife, but that turned out fruitless (there was actually no fruit as well) and I only managed to catch a few biodegradable slivers. So clearly there had to be another attack point. Well, the serrations of the knife turned out to be small enough to be bitten off. Then start at the top of the knife and work down. Chew long and hard, and miraculously your saliva actually begins to dissolve the knife. The human body is amazing.

By the way, if you were wondering what it actually tasted like (because I assume a normal reader probably does not intend to replicate such a procedure), it tasted kinda planty. Not really like wood though, but it really did feel better than the plastic toothbrush I tried to digest about two years ago (which, by the way, I ended up spitting out because I could not dissolve it). I assume a good part of it was plant-based materials (cellulose?) so I should be fine. I aborted the knife-eating procedure after around a third of a knife, partly because the dissolving part admittedly take quite a while, and partly because the next round starts soon.

Tournament Round @ 3:00: Interesting idea, except the logistics of this event weren’t very well thought out. Lots of chaos as to organizing the 32 teams takes about 20 minutes to settle down. At 10 minutes per set, that’s a downtime of about 67%, which is pretty bad to be honest. Further rounds take a bit less time to organize, but are still time-consuming; in the end BMT overran its schedule by well over an hour, leading to many of the losing teams leaving early. Not so great on the contest morale in general. Now onto the problems:

First set: #6 is pretty trivial; it is about multidimensional things. Although this is partly due to prior experience; in particular I dabbled in the subject by myself for a few days last year, concluding that the n-cube follows (x+2)^n generation procedure. Thus the “number of 3-cubes that compose a 5-cube” is simply the x^3 coefficient of (x+2)^5, and that is easy enough to compute. [Similarly, (x+1)^(n+1) describes the simplex aka tetrahedron aka triangle, and (2x+1)^n describes the cross polytope aka octahedron, although you do have to fudge the formula a bit to get the component numbers. No other regular polytope generalizes.]

By the way, that ended up degenerating into philosophical discussion on noninteger dimensions, which are technically evaluable by using the gamma function extension of the factorial, and most probably I alienated half of my viewers who go to my school by typing up random arcane math stuff. Although I’m not sure how they managed to survive the earlier portion. Oh well.

The rest of the set is somewhat easy as well, as #5 is a demonstration of the Pythagorean Theorem, and so on. Whoosh!

Second set: Oops, I expended what little energy I had regained during lunch on the first set. Completely fail easy linearity of expectations bash, then timesink on a few earlier problems. We get something like 3 problems, which definitely doesn’t advance, and thus we become another victim of the single elimination system.

That said, the single elimination system sucks on general tournament morale as well; this probably contributes greatly to the evacuation of most of the losing teams; teams like us were only occupied due to the existence of a chessboard.

Chess @ 4:00: After losing rather unceremoniously (we were 4th seed who lost to 13th seed), we decided to play chess. First, we tried to do so in the auditorium on one of the lecture tables, but those tables are seriously small and unstable. That led to the development of a miniature version of chess (4×6). Here’s the setup:







Maybe I swapped the queen positions, but that’s rather inconsequential.

Anyways, some rules: 1) Pawns cannot move twice on their first turn for semiobvious reasons 2) no castling 3) no enpassant 4) not sure how pawn promotion works, but since nobody’s ever done so before, that’s a moot point.

That game turned out to be a drawfest. Pawns locked places, queen trade rook trade rook trade pawn trade. Whee, a draw. I mean, I’m vastly incompetent at chess (mostly failing due to unwillingness to study opening theory) and believe that trading pieces is the best thing since sliced bread, and I managed to eke a draw.

Although, An.Zh. managed to win a game! Good job to him!

Later on, we migrate to more stable ground (right outside the auditorium) and we play a game of single-board bughouse. Basically, bughouse with two 4×8 boards. No queens (queens become royal kings) and rooks, bishops, and knights are distributed evenly. I think it was RNKB or RNBK, but I may be mistaken. But anyways, that lasts its course, and Aa.Li. comes up with a new variant:

So basically in this variant, the split board system semi-applies. However, each team controls a single color of pieces (why did I type “colour”?). You can only control pieces on your side though. This leads to a technique called “rook sniping” where you save up both players’ moves, and, in rapid succession, move twice to kill a piece without your opponent being able to react. (Actually, it’s not rook-specific, but rooks are pretty effective with this strategy… although the first piece to use this was a bishop if I recall correctly which took down a queen)


Awards @ 6:00: Remember, the awards ceremony was supposed to END at 6:00. Good job to Je.Wu. for not carelessing in individual round, and getting something like 5th! And darn we get 3rd team, getting $50 gift certificates specifically to a particular math course which is severely underlevelled, and likely costs more than $50. Those crafty salespeople! We’d actually be more content with 6th or 7th team, who got USB drives instead. Darn, they get tangible prizes 😦 But anyways, despite the disorganization, all is well.

Then we eat dinner, and go back home on BART again. Much contact ensued meanwhile. Oh, and we barely caught the train/bus with several seconds before it left 😀


Wow, that was long, and certainly probably does not justify the “semi-long” designation given in the title of my blog. Oh well.

I might actually expound further on the endurance issue later, but I hope you get somewhat of an idea why I don’t have any of it in the example posted earlier.