Schoolwork is really easy and short, I just do all te stuff in a few hours and that's set for the week. :D. No need for more time lol. Speaking of which my school grades are bad:
In addition to the B in compsci, my English grade has joined the B range after getting an 86 on an essay :o. Luckily this quarter's pass fail, so none of my grades count yay.
and mandarin is still absurd. The teacher's like "you need to record yourself saying this blah blah" and I'm like why are you forcing me to talk you've done enough of this during in person learning.
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I took HMIC yesterday. No discussion yet :|.
OMO: Also no discussion :| but MAHOGANY is OP.
I'm grinding so much math, since school closed, I did 182 hours of math. Literally, there was this day where I did 13 hours of math no joke. Mostly because I don't have stuff to do and I have OMO. Probably will do less math after OMO.
And finally USACO :bomb: . I'm so mad about the fact that I got a 600, with 10/3/6 on the problems. If I got one of #2 or #3 correct I wouldn't have to do USACO ever again. I wanted to pass so I would never have to USACO again, but now rip. I can't stand USACO. Doing it makes me depressed just like Chinese school back in elementary school.
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Other stuff: Contrib quiz #3 reminder: Quiz is here: https://forms.gle/54L9HCWDA8ZfwQgs7 Please take it!
Also, the AoPS attacks are getting out of hand, but tbh, I think the admins should stop censoring everything that comes up. I've saved the recent compilation, Instagram me for it: @kevininstz.
I'm now using blogger to save a copy of my blog posts - in case they get deleted. And, obviously, friends to post for me (I send what I want to post by blogger now).
But TBH the admins deserve to sorta be attacked, because whoever's attacking is definitely mad at them.
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Ok, now here we go: Top 5 Best Math Problems, 2019-2020 edition!
5. [quote = 2020 AIME I #5]Six cards numbered $1$ through $6$ are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order.[/quote]
When immediately seeing this problem, I just counted all the correct cases of increasement, getting 026. Later, I found my error of not seeing the decreasing case and got 052. I bashed out all 52 numbers when checking to make sure, and got it correct afterward. I liked this problem because it truly tested your combo knowledge and whether you were good at combo, although only a #5. For example, You-Know-Who missed this question, putting him at a dangerous 222 index, so I hope cutoff is 222.5 :D.
4. [quote=2020 CMIMC Geo #7]In triangle $ABC$, points $D$, $E$, and $F$ are on sides $BC$, $CA$, and $AB$ respectively, such that $BF = BD = CD = CE = 5$ and $AE - AF = 3$. Let $I$ be the incenter of $ABC$. The circumcircles of $BFI$ and $CEI$ intersect at $X \neq I$. Find the length of $DX$.[/quote]
I drew a diagram after seeing this question, having now only 15 minutes remaining. Seeing that DX is approximately 3 and that $AE-AF=3$, I just quickly guessed 3. Afterward, I was shocked when I realized that I GUESSED this question correct. First legit correct guess since 2018 AMC 10B #25.
3. [quote = 2020 AIME I #12]Let $n$ be the least positive integer for which $149^n-2^n$ is divisible by $3^3\cdot5^5\cdot7^7.$ Find the number of positive integer divisors of $n.$[/quote]
15 minutes before the AIME, I was reviewing a formula sheet in a study hall. Then, upon seeing this problem, I immediately thought to LTE, a formula that was on my sheet! The question was easy by that, and this made me feel so grateful about having reviewed the review sheet before AIME. If not for this question, I would have had a 228 index - unsure about JMO qualification.
2. [quote = 2020 AMC 10B #25]Let $D(n)$ denote the number of ways of writing the positive integer $n$ as a product$$n = f_1\cdot f_2\cdots f_k,$$where $k\ge1$, the $f_i$ are integers strictly greater than $1$, and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the number $6$ can be written as $6$, $2\cdot 3$, and $3\cdot2$, so $D(6) = 3$. What is $D(96)$?[/quote]
With only 3 minutes left, I went to this problem. Then, I proceeded to BASH BASH BASH. After bashing the numbers out, I got 71 - but wait, I forgot a case! Adding that case got.....112! That's an answer choice! I quickly put 112, leaving less than half a minute.
When we compared answers, it turns out that I somehow bashed CORRECTLY in 3 minutes! And everyone else failed so hard. If not for this problem, then 10B wouldn't have been as nice for me as it was here. I might not have beaten You-Know-Who on 10B.
1. [quote=2020 HMMT C6]Alice writes $1001$ letters on a blackboard, each one chosen independently and uniformly at random from the set $S=\{a, b, c\}$. A move consists of erasing two distinct letters from the board and replacing them with the third letter in $S$. What is the probability that Alice can perform a sequence of moves which results in one letter remaining on the blackboard?
[i]Proposed by Daniel Zhu.[/i][/quote]
Upon this question, I immediately tried small cases, with $1, 2, 3, 4, 5$ letters, and then saw a pattern with the numbers: $1$, $\frac23$, $frac23$, $\frac{20}{27}$, $\frac{20}{27}$. Then, I just assumed the formula for all odd $n$ letters was $\frac{3}{4}-\frac{1}{4 \cdot 3^{n-2}}$. At that point, I just plugged in $n=1001$ and finished.
I then found out that I somehow engineer's inductioned this question CORRECTLY, letting me onto top 50 for combo! And moreover, this question made the difference for me making HMIC! :-D And finally if not for this problem, Lexington Alpha would not have gotten tenth, beating TJ A by a mere bit! This problem literally changed everything for my day at HMMT.
