Bounded-Error Log

Here’s a guilty secret: I like getting feedback.

I’m not restricting myself to painstakingly thoughtful comments that attempt to build upon and transform the post to form an interesting conversation, the kind English teachers are hellbent on promoting. Sure, I get the most kicks out of those, but I’m not picky. Even single-digit pageview bars or a handful of Facebook “like”s give me buzzes of excitement.

It’s a guilty feeling, because I also think that that these are unimaginably cheap internet currencies and should not qualify as “meaningful” under a rational mindset. I strongly suspect visitors accidentally click on my blog and leave after five seconds without taking in anything, because I do that all the time to other people’s blogs and sites. Sometimes it is out of boredom, sometimes it is because I actually have something of higher priority to do than indiscriminate reading, sometimes it is simply because I cannot read the language. I’ve seen plenty of people like posts on Facebook based on the poster, only occasionally taking into consideration the first word of the post in question, before actually reading them.

Yes, the proliferation of “liking” on Facebook bothers me. I don’t expect everybody to reply meaningfully to everything when they just want to express approval lightly. However, when I see that tiny minority of people handing them out to people in their own threads like programs at a concert, I become indignant. Under their influence, what was originally a straightforward, meaningful badge of appreciation becomes a handwavy gesture that carries virtually no weight, and then I don’t know what to do when I see something I like seriously. Will clicking that button still express the feeling strongly enough?

I accept that, in our stressful world, a few instant effortless gags that take ten seconds to fully process and approve deserve a place. Nevertheless, the number of people who seem to want to make the “like” a completely passive and automatic action is almost physically painful:

This is a Fillomino puzzle where every polyomino is required to be an L-shape, as in Sashigane. Write a number in every empty cell so that every group of cells with the same number that is connected through its edges is an L-shape (with arms of positive length and 1-cell thickness) with that number of cells.

May be slightly reminiscent of no-rectangle Fillominoes. Slightly… (Has anybody done this before? It seems so interesting that I feel like I couldn’t be first.)

Yes. I know it’s been more than a month. Blogging motivation decreases, but the responsibility of that stay tuned doesn’t go away.

It’s okay. It’s all worth it because the stuff in the games room is absolutely ridiculous. Warning: huge post.

I made this a long time ago but put it off until I had programmed enough to digitize it without my fingers leaving the home row. I think the finish is interesting.

LITS - Nikoli. Exactly one tetromino per region, no 2x2s, they’re connected, adjacent tetrominoes are noncongruent.

Yeah, I lied last time I made one of these; the original Nikoli name wasn’t that hard to remember, and “sashigane puzzles” has shown up as a search query, so here you go. Perfect opposite-type-clue rotational symmetry, chaotic_iak! I hope you’re satisfied now.

Every time I notice that I have hoarded a large number of strange assignments and essays from another school year of work I get all guilty. First there’s the knowledge about ancient Chinese dynasties and plant hormones that I only have shadows of recollections of, which makes me wonder whether all the time and effort invested by teachers, classmates, and myself have gone wasted.

I know, though, that given that I still sense these shadows, it shouldn’t be difficult to look up and relearn this stuff if I ever need to do so. This brings me to the non-factual parts of the learning, such as writing skills with all its variations. There’s persuasive writing, which I don’t use much because I can’t usually even persuade myself to take a side in anything, let alone others. There’s descriptive writing mode, which I don’t use much because the most vividly describable things I encounter are food, and the shallowness of piling flowery adjectives together to talk about food just makes me cringe nowadays. Previously, I wrote at least two such compositions in sixth grade. Blech.

Day 2 of the contest.

Did you know that in Chinese [or Mandarin, whatever] “four” is unlucky because it’s a homophone for “death”, and hospitals tend to skip it in floors or ward numbers?

Did you know that there was going to be an anecdote involving the seventh Artemis Fowl book but I couldn’t make it work so instead you have a weird and utterly disconnected metareference to something deleted?

I don’t know, it sounded cool at the time.

Problem 4. Find all functions f: Z → Z such that, for all integers a,b,c that satisfy a+b+c = 0, the following equality holds: \[f(a)^2+f(b)^2+f(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).\] (Here Z denotes the set of integers.)

An innocent-looking functional equation, but once you start trying it you discover that there’s quite some depth to it. Random guessing can yield that \(f(x) = x^2\) is a solution, so I proved inductively that after dividing out a constant f(1) then the remaining part of f is a perfect square. Letting \(f(x) = f(1)g(x)^2\) with g(x) a nonnegative integer and factorizing the original equation, I got an auxiliary functional equation equivalent to the original equation.

Casework on small values of g, and the surprises started coming hard and fast. First: wow there’s an extra odd-even solution! Then: woah there’s another mod 4 solution! What is this madness?

I have just realized that I have only ever tried one level of difficulty in puzzle construction, viz., “as hard as I can make it”. This is mainly because I don’t want to construct anything overly trivial with the same few tricks, but, well, maybe it’s not the best idea for actually trying to build an audience.

Am I actually trying to build an audience? Am I? *shudders*

(Yajilin summary: fill in some cells, draw a loop through the rest, filled cells aren’t adjacent, arrows denote # of filled cells along some ray; MellowMelon’s rules)

I could spend all day coming up with post titles like this one. Really, I could. Anyway, after receiving the letter gently reminding me to turn in the official IMO report in Chinese, I finished that first and turned it in. This, plus the fact that I don’t have any way to do any of my summer homework yet, should make continued blogging much easier.

These months of preparation and anticipation, and in just over two days it will be behind us forever.

Thus were my thoughts at 3:30 in the morning, which were a much worse method of preparation than that which I used for the APMO, which involved trying for the first time to put my compass in its box and staring at a cryptic crossword. Twisted thoughts as I lay innocently in bed, trying to preserve my spirit and mathematical function. I got up at 6:30 and ate a breakfast nervously with the team.

We dispersed into the contest hall. Flat squarish white tables in orderly rows greeted us. They were considerably smaller than the arm-span tables we had last year in the Netherlands’ stadium, but the space was still ample compared to the ones we took our practice tests on at home. I floundered a bit looking for whoever was supposed to check our stuff for forbidden items, but none of the proctors paid any attention to that, so I flipped through my own jacket pockets paranoidly.

But preparation was too brief, and there were at least fifteen minutes left with nothing to do except try not to panic. I managed to fill these fifteen minutes by doing elaborate breathing exercises, raising and flapping my arms, counting down seconds, focusing on a color word, meditating badly, clearing out everything nonmathematical from my mind with a symbolic gesture. This is not a very coherent description, but I wasn’t feeling very coherent.

I opened an eye halfway and watched as the clock ticked down the last few seconds. The starting signal sounded. I opened up the problem envelope…

Again, the Zotmeister type. (Short rules: each cell states how many liars are in the 3x3 square centered at it, liars incorrectly so. Liars satisfy the “dynasty” rule i.e. liars are not orthogonally adjacent and non-liars are connected through sides.)