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My Two Cents – HCMOP 2012

HCMOP 2012

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My Two Cents – HCMOP 2012 | hcmop.wordpress.com Reviews

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HCMOP 2012

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1

Problem Solving Skills | My Two Cents

https://hcmop.wordpress.com/problem-solving-skills

Useful Books and Links. Here’s an archive of my posts sorted according to different topics. How to solve an Olympiad problem. Symmetric Polynomials ( 1. Lagrange’s interpolation formula. Factorisation using Sophie Germain’s Identity and Complex Numbers. Miscellaneous techniques in algebra. Tips for solving inequalities. A property of convex functions. Inequalities concerning sides of a triangle. Common replacements in solving functional equations. Importance of bijection in solving functional equations.

2

Number Theory | My Two Cents

https://hcmop.wordpress.com/number-theory

Useful Books and Links. Here are some essential concepts in number theory:. We use the identity. One can obtain the value of. Until both terms are equal. As a corollary, there exists integers. Are positive integers which are coprime, there exists integers such that. Fermat’s Little Theorem:. Is a prime, we have. Denote the number of positive integers less than. Given a system of simultaneous congruences in the form of. Are pairwise coprime positive integers, there exist integer solution. Leave a Reply Ca...

3

Another two interesting problems from SMO(O) First Round | My Two Cents

https://hcmop.wordpress.com/2012/05/30/another-two-interesting-problems-from-smoo-first-round

Useful Books and Links. Two interesting problems from SMO(S) First Round. SMO(J) Second Round Mock Paper 1 →. Another two interesting problems from SMO(O) First Round. May 30, 2012. Personally, I like problem 23 and 25 of the paper. I think I have seen both problems mentioned in some competition books before, and the solutions to these problems are pretty nice as compared to the brute nature of other problems. SMO(O) 2012 P23) The sequence. Is defined recursively by. Determine the value of. Would resembl...

4

Geometry | My Two Cents

https://hcmop.wordpress.com/geometry

Useful Books and Links. Has a right angle located at. Is a point on. Such that $ angle ABD = angle CAD$. We have. The area of triangle. Is given by the equation. Such that they are concurrent (intersect at a point). We have. Are on the sides. Respectively. Then line. Is collinear if and only if. Is a point on side. Are the circumcentre and incentre of triangle. Respectively, then we have. Are the circumradius and the inradius of the same triangle respectively. Consequently,. GIven a cyclic polynomial.

5

SMO(J) Second Round Mock Paper 1 | My Two Cents

https://hcmop.wordpress.com/2012/05/31/smoj-second-round-mock-paper-1

Useful Books and Links. Another two interesting problems from SMO(O) First Round. Proving Collinearity →. SMO(J) Second Round Mock Paper 1. May 31, 2012. SMO(J) Second Round Mock Paper 1. I was slightly surprised when things like Cauchy Schwarz Inequality came out in junior section. It’s kinda hard to expect the kind of questions which will appear in SMO right now. Solutions are also attached in the above link. This entry was posted in Random. Another two interesting problems from SMO(O) First Round.

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About me | PQToan's blog

https://combigeomery.wordpress.com/gioi-thieu

Toan Quang Pham (Phạm Quang Toàn) – student studying in Australia. Interested in olympiad mathematics (combinatorics, number theory). Like reading manga and watching HIMYM and Friends. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out. You are commenting using your Facebook account. ( Log Out. A good...

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IMO 2016 | PQToan's blog

https://combigeomery.wordpress.com/2016/07/23/imo-2016

Bài hình học Tuần 4 tháng 12 – 2015 của thầy Trần Quang Hùng. The normal approximation to the binomial distribution →. IMO 2016 was held from 6/7/2016 to 16/07/2016. Although I didn’t attend this, I just want to post my solutions and how I think about the difficulty of the problems, which can be found here. I will post my solutions on this post. Many awesome solutions can be found on AoPS. For which each cell of. Table can be filled with one of the letters. In such a way that:. And one third are. So we n...

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Reading a solution using algebraic integers of a HMMT number theory problem | PQToan's blog

https://combigeomery.wordpress.com/2017/01/05/reading-a-solution-using-algebraic-integers-of-a-hmmt-number-theory-problem

Yellowstone Permutation – St. Petersburg MO 2015, grade 9, 2nd round. Reading a solution using algebraic integers of a HMMT number theory problem. I tried to attack the following problem but eventually gave up. HMMT Ferb 2015 Team P9. Is an integer and find its remainder upon division by. In the second paragraph of the official solution (linked above), it said that the expression is “an integer-coefficient polynomial symmetric in the. And also syymmetric in the. Is symmetric polynomial in. Is symmetric p...

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phamquangtoan | PQToan's blog

https://combigeomery.wordpress.com/author/phamquangtoan

Math, manga, HIMYM and Friends. Reading a solution using algebraic integers of a HMMT number theory problem. I tried to attack the following problem but eventually gave up. Problem 1 (HMMT Ferb 2015 Team P9) Let and . Prove that is an integer and find its remainder upon division by The only idea I have is to … Continue reading →. Yellowstone Permutation – St. Petersburg MO 2015, grade 9, 2nd round. The normal approximation to the binomial distribution. Thầy Trần Quang Hùng có một chuyên mục Mỗi tuần một ...

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The normal approximation to the binomial distribution | PQToan's blog

https://combigeomery.wordpress.com/2016/08/24/the-normal-approximation-to-the-binomial-distribution

Yellowstone Permutation – St. Petersburg MO 2015, grade 9, 2nd round →. The normal approximation to the binomial distribution. A coin is flipped. Times with probability of getting heads is. This is a binomial approximation. The Year 12 MATH B textbook gives an normal approximation to this:. Or expected value) and. Is the standard deviation. Since the textbook doesn’t give a proof for this so I will go and prove. According to the definition, the expected value (or the mean) of getting heads is. Updates on...

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Yellowstone Permutation – St. Petersburg MO 2015, grade 9, 2nd round | PQToan's blog

https://combigeomery.wordpress.com/2016/10/03/yellowstone-permutation-st-petersburg-mo-2015-grade-9-2nd-round

The normal approximation to the binomial distribution. Reading a solution using algebraic integers of a HMMT number theory problem →. Yellowstone Permutation – St. Petersburg MO 2015, grade 9, 2nd round. This problem was given to the St. Petersburg Olympiad 2015, 2nd round, grade 9 and is known as Yellowstone Permutation. You can see here. For the article about this sequence and here. For the OEIS entry. A sequence of integers is defined as follows:. But not relatively prime to. Suppose that for all.

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My Two Cents – HCMOP 2012

Useful Books and Links. December 13, 2012. Sorry for the long six months hiatus. I have been involved in lots of bridge activities as well as university commitments in this six months. I realise that my brain has became quite rusty after not doing Math Olympiad for half a year. Now that I am back, I will try update as often as possible and get my brain functioning again. The first technique involves identifying a common angle between two lines. Suppose you want to prove that the three points. The last eq...

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hcmorava.cz | Další web používající WordPress

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hcmorethanmusic

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