Finn Hulse's Messageboard

Everybody else is doing it, I might as well. Enjoy! :D

#Finn #Messageboard #Socialize

Note by Finn Hulse
7 years, 1 month ago

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  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
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2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Does your school have a strange schedule/lots of free periods? You seem to be able to get to a computer at all times of the day, I've been curious how you manage that with school/homework.

Sam Solomon Staff - 7 years, 1 month ago

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HAHAHAHAHAHAHA! Yes, I have no life, and yes, except today, I spend roughly 2 hours on Brilliant. Which is tough because I'm preparing for a Bar-Mitzvah and I'm swimming. So yeah. I am a Brilliantic for life.

Finn Hulse - 7 years, 1 month ago

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Nice, it's pretty funny how you said you had no life, my friends tell me that all the time and make fun of me for getting on this website a lot. There all like, " oh ya Robert, your website is only for brilliant people. In a stupid sarcastic tone. Didn't know you were Jewish, that's pretty cool! What's your plan for your Bar-Mitzvah. My friend went to a nice hotel in Mexico and ate a ton of food. He said it was pretty freaking amazing.

Robert Fritz - 7 years, 1 month ago

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@Robert Fritz The service is gonna be pretty regular, with a frickin wild party after. For my B'nai-mitzvah, or "good deed", I'm tutoring a bunch of 5th graders about MATHCOUNTS and problem-solving techniques so that they're prepared to be on the MATHCOUNTS team in middle school. It's frickin boss, dude. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Sweet! I also have to ask, have you ever tried science bowl. I'm stuck between doing track, science bowl, or mathcounts . Plus I just found out that for the science and math competitions that my magnet school can't compete in them as a team I was like, " what the **!" Luckily, I heard my other school actually has a decent team. I guess I'll try it next year. Is it only 7th-8th grade. Geez, I have to many unanswered questions.

Robert Fritz - 7 years, 1 month ago

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@Robert Fritz No, I've never done Science Bowl. But you should totally do MATHCOUNTS! It's fricking boss! :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse National Science Bowl (NSB) is something you should really consider doing! It was really fun last year. Do it for the experience.

Daniel Liu - 7 years, 1 month ago

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@Daniel Liu How do I get started?

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Science bowl is the best, I first got started in our schools science bowl club, it is really fun and you learn a lof different subects of science ask your teachers about it.

Mardokay Mosazghi - 7 years, 1 month ago

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@Mardokay Mosazghi Oh. My school doesn't have a Science Bowl club. Can I still participate?

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Yeah I think so

Mardokay Mosazghi - 7 years, 1 month ago

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@Mardokay Mosazghi They have nothing like that in Australia. It's saddening.

Sharky Kesa - 7 years, 1 month ago

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@Sharky Kesa I feel sorry for you, but do you have any math competitions, You are 13 years old and you are level 5 in algebra, combinactoris and number theory.Nice!

Mardokay Mosazghi - 7 years, 1 month ago

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@Mardokay Mosazghi I have a couple which I am going to attend and also I am 12.

Sharky Kesa - 7 years, 1 month ago

That's what I've been thinking as well... then I remembered how blissfully delightful middle school was. Not much homework there.

Justin Wong - 7 years, 1 month ago

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HAHAHAHAHA yeah. I haven't done any homework AT HOME since 4th grade. No joke. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Same here I complete my homework at school and then either log on to Brilliant or enjoy

Ashtik Mahapatra - 7 years, 1 month ago

@Finn Hulse gosh y'all are so lucky; in Taiwan, we have like 2 hours of homework everyday (as in, at home).... -.- not to mention tests every three or so days.... uggg

dana chiueh - 7 years, 1 month ago

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@Dana Chiueh :O

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse This is usually what happens in south and south-east Asia. I have done Kindergarten in India, I know (though not that much).

Sharky Kesa - 7 years, 1 month ago

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@Sharky Kesa yup (although, technically, Taiwan is in east asia....)

dana chiueh - 7 years, 1 month ago

@Sharky Kesa I went to the American Embassy School in Dehli. Needless to say, it was luxurious and easy. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse ..........oh it's the "American Embassy" part eh?

dana chiueh - 7 years, 1 month ago

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@Dana Chiueh Hmmm...

Sharky Kesa - 7 years, 1 month ago

@Finn Hulse i know it's so sad D:

dana chiueh - 7 years, 1 month ago

@Dana Chiueh Me too

Mardokay Mosazghi - 7 years ago

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@Mardokay Mosazghi Dude you're in the US. :P

Finn Hulse - 7 years ago

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@Finn Hulse What if it's a special sort of school such as a selective school for highly academic or a grammar school.

Sharky Kesa - 7 years ago

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@Sharky Kesa He goes to Takoma Park. :P

Finn Hulse - 7 years ago

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@Finn Hulse no i got MBHS

Mardokay Mosazghi - 7 years ago

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@Mardokay Mosazghi Oh. But you used to go to Takoma right?

Finn Hulse - 7 years ago

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@Finn Hulse yep

Mardokay Mosazghi - 7 years ago

What do you like to do except "Brilling".!

Satvik Golechha - 7 years, 1 month ago

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Math... and friends. Haha, I hadn't thought of Brilling. :D

Finn Hulse - 7 years, 1 month ago

What is there to do in Willamsburg?

Calvin Lin Staff - 7 years, 1 month ago

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Quite a lot! I just don't do any of it. Have you ever heard of Colonial Williamsburg? It was the capital for twice as long as Washington, D. C..

Finn Hulse - 7 years, 1 month ago

are you really 13 years old? :D

Nisarg Thakkar - 7 years, 1 month ago

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Uhh. Well im not ;) (5th grade)

David Lee - 7 years, 1 month ago

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good! Great going :) hope you guys become renowned for doing something better and new. All the best for Life and its challenges! School is way awesome and Youth is gr8. But when it goes, you know where you stand and I hope, then you know where you want to go next.

Nisarg Thakkar - 7 years, 1 month ago

HAHAHAHAHAHAHAH nice. Fist bump for us young people. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse :D Youth is beast.

Sharky Kesa - 7 years, 1 month ago

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@Sharky Kesa :D

Finn Hulse - 7 years, 1 month ago

Finn Hulse .....hv guts attempt this

MAYYANK GARG - 7 years, 1 month ago

@Finn hulse How/when you noticed you're smart in (math/physics &others...) at the first time ? How did u feel then? :)

Mahdi Al-kawaz - 7 years, 1 month ago

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I've always liked math a lot, but when I got to sixth grade, I realized it was cool to be really good at math. So I started becoming "fake"-good, at math just to be cool.

I realized that in fact, math was AWESOME in the summer after sixth grade. Now, I'm in 7th grade, and I do math because of how interesting and amazing it is.

Finn Hulse - 7 years, 1 month ago

Hi @Finn Hulse , it seems like you are very eager to be on the "People to Follow", hope you won't want to bite my head off for taking the place, haha. What I want to say is, "People to Follow" isn't a place to get attention, nor judging your achievements/ability. You are doing great and the "People to Follow" doesn't matter very much actually! Keep up your great job, cheers!

Christopher Boo - 7 years, 1 month ago

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Haha, yes I am very eager to get on that list! I think your head should be pretty safe, though. It's just a matter of pride, for me. You know, like I just want to be considered a person to follow! Don't we all? :D

Finn Hulse - 7 years, 1 month ago

You should get an AoPS account.

David Lee - 7 years, 1 month ago

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I have one, it's FINNN.

Finn Hulse - 7 years, 1 month ago

Hey, I am not god! :P

David Lee - 7 years, 1 month ago

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Dude. I will treat you as such.

Finn Hulse - 7 years, 1 month ago

man! finn hulse! u r juss 13 yrs old nd u solve so many problems of higher levels with ease...! gr8! :) salute

Pradeep Ch - 7 years, 1 month ago

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Thanks, you made my day! Actually, I'll be 13 in May. But yeah, I'm totally cool solving problems for fun, but on tests, I freak out and get a lot wrong. :D

Finn Hulse - 7 years, 1 month ago

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oh ! den u r 12.... den a bigger salute...

Pradeep Ch - 7 years, 1 month ago

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@Pradeep Ch Haha, okay. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Just a salute? I admire you Finn Hulse dude you are awesome. I mean I am 15 and still I can't solve many problems but you , what can I say, FAB. I think this proficiency comes from AoPS. Am I right?

Ashtik Mahapatra - 7 years, 1 month ago

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@Ashtik Mahapatra Hahaha, if you say so.

Finn Hulse - 7 years, 1 month ago

@Ashtik Mahapatra Oh actually no, I've never really used AoPS. I can't figure out how to get anywhere. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse I also have an AoPS acc but I am confused its so messed up

Ashtik Mahapatra - 7 years ago

Happy (belated) birthday Finn!!! Finally 13 :D I'm turning 13 in twelve more days (May 18)...

dana chiueh - 7 years, 1 month ago

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Aww thanks dude! :D

Finn Hulse - 7 years, 1 month ago

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:) no prob

dana chiueh - 7 years, 1 month ago

Happy (probably belated) birthday, Finn!!!!! You're 13 and a teenager!!! I have 7 more months to wait.

Sharky Kesa - 7 years, 1 month ago

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Lol, I'm almost there (twelve more days!~)

dana chiueh - 7 years, 1 month ago

@Finn Hulse Congrats on your level 4 and level 5 on all subjects especially calculus.

Mardokay Mosazghi - 7 years ago

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Oh yeah thanks. As a matter of fact, when I first joined Brilliant (with all Level 2's and 3's and 1's) I was originally Calculus Level 5. There was a really easy problem on the placement test. I accidentally lost it for a while, but then one of my wrong answers to @Sharky Kesa's Level 4 problem turned out to be right after all and my rating got pushed up! :D

Finn Hulse - 7 years ago

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Which question was this?

Sharky Kesa - 7 years ago

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@Sharky Kesa It was asking for ζ(0.5)\zeta(0.5) where you had like the sign switched or something.

Finn Hulse - 7 years ago

Hugh Everett hypothesized that objective reality is actually many worlds, every event being a branch point spawning ever more possible worlds, so that in one world, the cat is alive, and in another, it's dead. Would you be a confirmation of that hypothesis, being that you seem to be everywhere and doing everything all at once?

Michael Mendrin - 7 years ago

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That is interesting to think about. And yes, I am doing a lot at once. Yesterday I had my Bar Mitzvah... :O

Finn Hulse - 7 years ago

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Mazel Tov!, to at least one of you anyway.

Michael Mendrin - 7 years ago

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@Michael Mendrin Haha thanks. Yes I think roughly 1100000\dfrac{1}{100000} of the currently existing universes contain a Finn Hulse who just had a Bar Mitzvah.

Finn Hulse - 7 years ago

Hi Finn have you noticed that it is showing that you have followed only 51 members. Actually you had followed around 3000+ I suppose?

Ashtik Mahapatra - 7 years, 1 month ago

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Yeah. I thought it was a bug but it wasn't. Did you spend all your time unfollowing people?

Sharky Kesa - 7 years, 1 month ago

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No I didn't . Why would I do that?

Ashtik Mahapatra - 7 years, 1 month ago

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@Ashtik Mahapatra Was talking to Finn. Sorry Ashtik for the miscommunication.

Sharky Kesa - 7 years, 1 month ago

No! It is a bug! :O

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Yeah it is

Ashtik Mahapatra - 7 years, 1 month ago

@Sharky Kesa @Trevor B. That was the most freaking boss game of FTW! ever! We have to do that more. :D

Finn Hulse - 7 years, 1 month ago

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Definitely.

Sharky Kesa - 7 years, 1 month ago

What's FTW?

Finn C - 4 years, 12 months ago

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YO FINN!!! For The Win. :D

Finn Hulse - 4 years, 12 months ago

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@Finn Hulse Haha... I guess its rhyme time. :D

Finn C - 4 years, 12 months ago

@Finn Hulse Nice name BTW... (I'm talking about the Finn part... The Hulse part is... ok I guess)

Finn C - 4 years, 12 months ago

@Daniel Liu @William Cui @Franklyn Wang @Akshaj Kadaveru @Nicky Sun You guys! Good luck at Nationals! I can't wait to watch the CD round on ESPN! It's going to be so intense! Watch out for Colin Tang! :D

Finn Hulse - 7 years, 1 month ago

@Dan Lawson Would you mind writing a solution to Plugging Roots into Functions? I'm really interested to see your technique. :D

Finn Hulse - 7 years, 1 month ago

@Yan Yau Cheng When will JOMO 4 results be released? I really want to know how @Emery Shelly and I did! :D

Finn Hulse - 7 years, 1 month ago

@Calvin Lin Could you boost the rating of Dominoes and Chessboards to like, 2200? It's pretty insanely tough until you realize the trick and then it's (moderately) easy. Good luck solving it! :D

Finn Hulse - 7 years, 1 month ago

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Is that so? I don't really think it is that hard at all... I will post a solution.

Daniel Liu - 7 years, 1 month ago

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Oh awesome! :D

Finn Hulse - 7 years, 1 month ago

Congratulations @Christopher Boo for beating me in terms of followers! I knew you would eventually, especially since you made "Who to Follow" and I didn't. Well, well, I guess I'll never be as good as you.

Finn Hulse - 7 years, 1 month ago

@Peter Taylor I'm happy to see that new bar where you can access solutions! I'm glad I don't need to upgrade to Brilliant Squared to have access to this decent little feature!

Finn Hulse - 7 years, 1 month ago

@Peter Taylor With the new solution-viewing format (where you can see what solutions you've posted) I had a "Brilliant" thought. What if when you viewed the page, beside each solution, it showed how many upvotes it had? Also, will you guys make it so we can view everybody's solutions, not just our own?

Finn Hulse - 7 years, 1 month ago

@Finn Hulse I found someone who follows more people than you: @Santanu Banerjee

Daniel Liu - 7 years ago

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Yeah, I had noticed that but assumed Finn knew.

Sharky Kesa - 7 years ago

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Yeah I did @Daniel Liu but can you find anybody with more comments than me? I'm like the most social person on the site. :D

Finn Hulse - 7 years ago

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@Finn Hulse There should be a couple.

Sharky Kesa - 7 years ago

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@Sharky Kesa I don't think so dude! I haven't seen anybody with like more than 500!

Finn Hulse - 7 years ago

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@Finn Hulse How about some of the staff? You can't see how many comment they have made.

Sharky Kesa - 7 years ago

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@Sharky Kesa Yeah I know that is a problem. :O

Finn Hulse - 7 years ago

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@Finn Hulse If it was possible they would have millions of comments @Finn Hulse

Mardokay Mosazghi - 7 years ago

@Emil Svensson Do you actually live in Williamsburg VA?

Finn Hulse - 7 years ago

@Calvin Lin Have you actually received my email? Sorry to bug you, but I'm interested to see your reaction. :O

Finn Hulse - 7 years ago

@Calvin Lin How is the rating for Plugging Roots into Functions Level 3? Only 16/32 people have solved it which should make it Level 4-5. :/

Finn Hulse - 7 years ago

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Recall that your problem had a wrong answer, and hence had an inflated rating. When we corrected it, the ratings were then pushed down. Given that it simply uses Newton formula, it's definitely not in level 5.

There is a possibility that the numbers are not accurate, given that we had to change the answer.

Calvin Lin Staff - 7 years ago

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I see. But the numbers were unchanged, so I don't think that that would have done anything. Especially considering that the moment you changed the answer, the # of solvers went from 1 to 16. But Newton's Sums is still a Level 4 concept, especially in that application of it. I'd appreciate it if you gave it the correct rating. Thanks. :D

Finn Hulse - 7 years ago

@Yan Yau Cheng I have a much simpler proof for problem #5.


Question Statement:

Given that pp and p2+8p^2 + 8 are both primes , what is the sum of all possible values of pp?


Solution:

We can see that if p1p \equiv 1 or p2(mod3)p \equiv 2 \pmod{3}, then p2p^2 will be congruent to 11 or 44 modulo 33, respectively (which is simply 121^2 and 222^2). In both of these cases, by adding 88 which is 1(mod3)\equiv -1 \pmod{3}, the expression is 0(mod3)\equiv 0 \pmod{3} and is thus never prime (it's divisible by 33). For p0(mod3)p \equiv 0 \pmod{3}, the expression is congruent to 0+82(mod3)0+8 \equiv 2 \pmod{3} which may or may not be prime. But because 33 is the only prime divisible by 33, we can just plug that in, which is 32+8=173^2+8=17 which is prime. Thus 3\boxed{3} is the only solution.

Finn Hulse - 7 years ago

Whew, I'm not very active recently and I just found that you are all most level 5 in every topic! Do you have a great source to learn your physics?

By the way, I like your tag #Finn, added to my list! :P

Christopher Boo - 7 years ago

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Yes! I attribute my recent change mostly to Brilliant Squared, though. Aside from that, @Anish Puthuraya's YouTube channel has been a great resource, along with Khan Academy and a Physics II for Dummies textbook. When I'm unfamiliar with an approach, Google is very helpful, and once I master a formula, I can apply it!

Oh yeah but also the thing about Brilliant Squared is that the problems are ranked way higher than they should be. I think it's mostly because the staff can choose the rating, even though in reality it gets pushed down a ton.

Oh yeah and #Finn is a pretty epic tag. :D

Finn Hulse - 7 years ago

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Thanks! :D

Christopher Boo - 7 years ago

I added that tag the moment I realized you could add any tag to your homepage. :D

Yuxuan Seah - 7 years ago

My mom speaks Mandarin and I was wondering how you pronounce your last name, since I don't think it's in pinyin.

Finn Hulse - 7 years ago

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@Yuxuan Seah.

Finn Hulse - 7 years ago

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Oh. My name is Yuxuan (Yû Xuān) and Seah is my family name. In pinyin it's Shé. I don't really know how to tell you how to pronounce it in English, because when people first see it, they usually get it wrong and I just adopt a Trial and Error method to help them get it right. But I could try :D

'See-ahh.' That's somewhat right. (My Chinese name, in case you wanna know, is 佘宇轩.) :D Try to teach yourself mandarin. It's fun. And educational. :D

Yuxuan Seah - 7 years ago

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@Yuxuan Seah Sorry about the formatting though, for the 'û' the sign on top is actually inverted. (Couldn't get it right on my computer. D:) And yes, 'Seah' isn't in pinyin. o.O Interesting that you ask such a question. :D

I didn't know your mom speaks Mandarin! Hmm... is she from China? Or Singapore? :D

Yuxuan Seah - 7 years ago

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@Yuxuan Seah Well, names are complicated. Check this out: http://en.wikipedia.org/wiki/Wolfe+585,_Senior

Yuxuan Seah - 7 years ago

Aww Finn, did'cha unfollow me? D: and what happened to Theme based problems. And hows the country ur in XP

Charlton Teo - 6 years, 11 months ago

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He hasn't left the country, I think, but the state. I am in a different country, SINGAPORE! :D

Sharky Kesa - 6 years, 11 months ago

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COME VISIT RI XD even tho im not sure if they allow strangers in

Charlton Teo - 6 years, 11 months ago

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@Charlton Teo I don't think I can. Go to the Science building in Jurong East tomorrow, you might see me in the afternoon.

Sharky Kesa - 6 years, 11 months ago

Hi Finn, did you take any math lessons outside the school? (i.e KUMON)

Ahmad Naufal Hakim - 6 years, 3 months ago

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Yes, a senior from the local college that my parents teach at comes over once a week to tutor me in advanced graduate-level math.

Finn Hulse - 6 years, 3 months ago

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Dude, you came back! Where have you been?

Sharky Kesa - 6 years, 2 months ago

That sounds really neat and fun, did your school has some kind of program that teaches you in math too? And how many times did you practice in a week? Sorry for asking too many questions, I'm just too curious ><

Ahmad Naufal Hakim - 6 years, 2 months ago

Hi

Will you post a question anytime soon ?

A Former Brilliant Member - 6 years, 2 months ago

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Sure!

Finn Hulse - 6 years, 2 months ago

@Mardokay Mosazghi Dude, I loved this problem Super Finn to the Rescue. And yes, I love trampoline tricks. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse Thanks

Mardokay Mosazghi - 7 years, 1 month ago

@Calvin Lin Have you seen this epic problem!? I think it's really cool and takes advantage of one of the coolest algebraic principles that I know! You'll enjoy it! :D

Finn Hulse - 7 years, 1 month ago

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Several edits are needed.

1) g(x)g(x) is a polynomial, otherwise I can define g(3) |g(3) | to be anything.
2) The degree of g(x)g(x) matters, otherwise we can take the square.
3) The leading coefficient of g(x) g(x) matters, otherwise we can just multiply by 2.

Calvin Lin Staff - 7 years, 1 month ago

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Okay. Wow. Dang, you're good. :O

Finn Hulse - 7 years, 1 month ago

What do you mean the degree of g(x)g(x) matters?

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse The polynomial g(x)=(5(3)5+3(3)411(3)32(3)2+3(3)+5)2 g(x) = (5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2 will also satisfy your conditions as previously stated, namely that each of the roots of g(x) g(x) is the reciprocal of one of f(x) f(x) roots.

Note that currently, saying "the coefficient of x5x^5 is -5 is also not sufficient, since I could take g(x)=A(5(3)5+3(3)411(3)32(3)2+3(3)+5)2 g(x) = A(5(3)^5+3(3)^4-11(3)^3-2(3)^2+3(3)+5) ^2 for some suitable constant AA.

Note that you will also need the condition that "each of f(x) f(x) roots are the reciprocal of g(x) g(x) roots", otherwise, I can just take αx1 \alpha x - 1 , where f(α)=0 f( \alpha ) = 0 .

The issue with some of your problems is that they are not correctly and clearly phrased. You have an idea of what it is in your head, but when written down, it could be interpreted in a multitude of ways. You need to take care of such 'edge cases' that I listed out above, instead of expecting others to deduce what you are thinking. They will not do so, and would instead just skip your problem.

Calvin Lin Staff - 7 years, 1 month ago

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@Calvin Lin It's all Greek to me. Would you mind making the changes? I'm sorry for the inconveniences with all of these problems. I'll make sure to not make such silly mistakes in the future. :D

Finn Hulse - 7 years, 1 month ago

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@Finn Hulse I've made some changes which makes g(x) g(x) uniquely determined (up to sign). There are possibly better ways of expressing it that are not so clunky.

I avoided talking about the "content of the polynomial", as that is not a commonly understood term.

Calvin Lin Staff - 7 years, 1 month ago

Finn, can you please tell me what is the line between 10 and Euler's totient function in your problem "Let's compute this manually " in your " Modular arithmetic and NT problems " set ?

Sriram Venkatesan - 6 years, 11 months ago

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aba|b means that aa is divisible by bb.

Sharky Kesa - 6 years, 11 months ago

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thank you ....

Sriram Venkatesan - 6 years, 11 months ago

No it means the opposite. So like 3123 \mid 12.

Finn Hulse - 6 years, 10 months ago

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@Finn Hulse LOL, fail! Could be used in the thing.

Sharky Kesa - 6 years, 10 months ago
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