IMO Math

From now on, I will post one IMO shortlist, then two of these below.        1 : "EGMO" ,     2 : "Romanian Masters of Mathematics" ,     3 : "Tournament of Towns" ,     4 : "USA ELMO Shortlist" ,     5 : "USA Math Prize for Girls Olympiad" ,     7 : "USAJMO" ,     8 : "Canada National Olympiad" ,     9 : "China TST" ,     10 : "India IMO Training Camp" ,     11 : "India National Olympiad" For example, it could go like: 2021 IMO #1, 2019 EGM0 #2, China TST #3.

Thanks for 1600 views, everybody! Keep viewing this blog!

Everyone has trouble with math olympiad problems, but what makes the difference is what you do  after .  Below are steps you should do (in order) if you do not know how to solve a problem.  1. Keep thinking about the problem until you completely run out of ideas, and you have tried every single one and it hasn't worked. Don't let any idea go; e 2. Okay, now it's time to give up. Read the solution carefully and understand every step of it. Don't think about the motivation for it yet.  3. When you have finished reading the solution and have verified that it is correct, in your mind summarize what they did, yet without thinking about the motivation. 4. Now, think about what the 'key' in the solution was, or what the 'heart of the problem' was. Basically, think about the main insight in the solution after which it got easy. Make sure to remember this 'insight', because it will apply to many, many other problems than just this one. 5. After a couple d

I will be posting higher quality math olympiad problems from now on. Using the random math olympiad problem generator Python program (which I had posted before), most problems are not high quality.  So, in the Python code, I have now removed the olympiads that do not have many good problems.  My updated list from which the computer randomizes looks like this:    1 : "IMO Shortlist" ,   2 : "IMO Shortlist" ,   3 : "APMO" ,   4 : "Austrian-Polish" ,     5 : "Balkan MO Shortlist" ,     6 : "Balkan MO Shortlist" ,     7 : "Baltic Way" ,     8 : "Benelux" ,     9 : "EGMO" ,     10 : "Iranian Geometry Olympiad" ,     11 : "Romanian Masters of Mathematics" ,     12 : "Silk Road" ,     13 : "Tournament of Towns" ,     14 : "USA BAMO" ,     15 : "USA ELMO Shortlist" ,     16 : "USA ELMO Shortlist" ,     17 : "USA USEMO" ,     1

 It is now officially the very first moment of 2022 (in EST).  Welcome, 2022! I hope you bring great happiness and health to everyone.  Time to eat cake.  via GIPHY

It is the last moment of 2021. The very last. Do your last farewells. I thank God and my parents for all the opportunities they have given me during this year.  And I hope me and everyone get even better ones in the coming year.  After this, no more 2021.  I would like to share a meme at this moment.  On this occasion, I am solving 2021 IMO #6; as the last of 2021.  Let $m\ge 2$ be an integer, $A$ a finite set of integers (not necessarily positive) and $B_1,B_2,...,B_m$ subsets of $A$. Suppose that, for every $k=1,2,...,m$, the sum of the elements of $B_k$ is $m^k$. Prove that $A$ contains at least $\dfrac{m}{2}$ elements. Let $A=\{a_1, a_2, a_3, \dots, a_n\}$. Note that for some number $0 \leq N \leq m^{m+1} - m$ with $m | N$, we can choose integers $x_{1}, x_{2}, \ldots x_{m}$ so that $$0 \leq x_{i} < m$$ and \[N = x_{1}m + x_{2}m^{2} + \ldots + x_{m}m^{m}.\] We know this by dividing both sides by $m$ and then writing $N$ in base $m$. Next, notice that we can write $N$ as the sum

I won't be posting any more problems today until 11:59 PM EST.  At 11:59 PM, I will post a very unique problem that is suitable for this day.  Take a wild guess for what it could be  😉

Hello,  Thanks for 1000 views of this blog over just a few days!  Be sure to read my solutions to the problems posted by clicking "Read more" on the post. I'm sure you will find them very interesting.  Please keep visiting my blog!  

December 29th, 1979 is when my mom was born, and yesterday was her birthday. I am solving the 1989 IMO SL #29 in honor of her 🙂 (oops i forgot to do this yesterday). I would solve 1979 IMO SL #29, but it doesn't exist because there were only 26 problems for that shortlist.  Happy Birthday Mama!

I have been working on this Python program that randomizes and gives a math Olympiad problem per run. This is what I use to determine which problem I will do.  You can see the code below and run it either on your computer or at repl.it .