diff --git "a/IMO/md/en-IMO-2020-notes.md" "b/IMO/md/en-IMO-2020-notes.md"
new file mode 100644--- /dev/null
+++ "b/IMO/md/en-IMO-2020-notes.md"
@@ -0,0 +1,270 @@
+
+# IMO 2020 Solution Notes  
+
+Evan Chen 《陳誼廷》  
+
+18 October 2025  
+
+This is a compilation of solutions for the 2020 IMO. The ideas of the solution are a mix of my own work, the solutions provided by the competition organizers, and solutions found by the community. However, all the writing is maintained by me.  
+
+These notes will tend to be a bit more advanced and terse than the "official" solutions from the organizers. In particular, if a theorem or technique is not known to beginners but is still considered "standard", then I often prefer to use this theory anyways, rather than try to work around or conceal it. For example, in geometry problems I typically use directed angles without further comment, rather than awkwardly work around configuration issues. Similarly, sentences like "let \(\mathbb{R}\) denote the set of real numbers" are typically omitted entirely.  
+
+Corrections and comments are welcome!  
+
+## Contents  
+
+0 Problems 2  
+
+1 Solutions to Day 1 3  
+
+1.1 IMO 2020/1, proposed by Dominik Burek (POL) 3  
+
+1.2 IMO 2020/2, proposed by Belarus 4  
+
+1.3 IMO 2020/3, proposed by Milan Haiman (HUN), Carl Schildkraut (USA) 6  
+
+2 Solutions to Day 2 8  
+
+2.1 IMO 2020/4, proposed by Tejaswi Navilarekallu (IND) 8  
+
+2.2 IMO 2020/5, proposed by Oleg Košik (EST) 10  
+
+2.3 IMO 2020/6, proposed by Ting- Feng Lin, Hung- Hsun Hans Yu (TWN) 11
+
+
+
+## Problems  
+
+1. Consider the convex quadrilateral \(ABCD\) . The point \(P\) is in the interior of \(ABCD\) . The following ratio equalities hold:  
+
+\[\angle PAD:\angle PBA:\angle DPA = 1:2:3 = \angle CBP:\angle BAP:\angle BPC.\]  
+
+Prove that the following three lines meet in a point: the internal bisectors of angles \(\angle ADP\) and \(\angle PCB\) and the perpendicular bisector of segment \(AB\) .  
+
+2. Let \(a \geq b \geq c \geq d > 0\) be real numbers satisfying \(a + b + c + d = 1\) . Prove that  
+
+\[(a + 2b + 3c + 4d)a^{a}b^{b}c^{c}d^{d}< 1.\]  
+
+3. There are \(4n\) pebbles of weights \(1,2,3,\ldots ,4n\) . Each pebble is coloured in one of \(n\) colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two piles so the total weights of both piles are the same, and each pile contains two pebbles of each colour.  
+
+4. There is an integer \(n > 1\) . There are \(n^2\) stations on a slope of a mountain, all at different altitudes. Each of two cable car companies, \(A\) and \(B\) , operates \(k\) cable cars; each cable car provides a transfer from one of the stations to a higher one (with no intermediate stops). The \(k\) cable cars of \(A\) have \(k\) different starting points and \(k\) different finishing points, and a cable car which starts higher also finishes higher. The same conditions hold for \(B\) . We say that two stations are linked by a company if one can start from the lower station and reach the higher one by using one or more cars of that company (no other movements between stations are allowed). Determine the smallest positive integer \(k\) for which one can guarantee that there are two stations that are linked by both companies.  
+
+5. A deck of \(n > 1\) cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards. For which \(n\) does it follow that the numbers on the cards are all equal?  
+
+6. Consider an integer \(n > 1\) , and a set \(S\) of \(n\) points in the plane such that the distance between any two different points in \(S\) is at least 1. Prove there is a line \(\ell\) separating \(S\) such that the distance from any point of \(S\) to \(\ell\) is at least \(\Omega (n^{-1 / 3})\) .  
+
+(A line \(\ell\) separates a set of points \(S\) if some segment joining two points in \(S\) crosses \(\ell\) .)
+
+
+
+## \(\S 1\) Solutions to Day 1  
+
+## \(\S 1.1\) IMO 2020/1, proposed by Dominik Burek (POL)  
+
+Available online at https://aops.com/community/p17821635.  
+
+## Problem statement  
+
+Consider the convex quadrilateral \(ABCD\) . The point \(P\) is in the interior of \(ABCD\) . The following ratio equalities hold:  
+
+\[\angle PAD:\angle PBA:\angle DPA = 1:2:3 = \angle CBP:\angle BAP:\angle BPC.\]  
+
+Prove that the following three lines meet in a point: the internal bisectors of angles \(\angle ADP\) and \(\angle PCB\) and the perpendicular bisector of segment \(AB\) .  
+
+Let \(O\) denote the circumcenter of \(\triangle PAB\) . We claim it is the desired concurrency point.  
+
+![](data:image/jpeg;base64,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)
+  
+
+Indeed, \(O\) obviously lies on the perpendicular bisector of \(AB\) . Now  
+
+\[\angle BCP = \angle CBP + \angle BPC\] \[\qquad = 2\angle BAP = \angle BOP\]  
+
+it follows \(BOPC\) are cyclic. And since \(OP = OB\) , it follows that \(O\) is on the bisector of \(\angle PCB\) , as needed.  
+
+Remark. The angle equality is only used insomuch \(\angle BAP\) is the average of \(\angle CBP\) and \(\angle BPC\) , i.e. only \(\frac{1 + 3}{2} = 2\) matters.
+
+
+
+## \(\S 1.2\) IMO 2020/2, proposed by Belarus  
+
+Available online at https://aops.com/community/p17821569.  
+
+## Problem statement  
+
+Let \(a\geq b\geq c\geq d > 0\) be real numbers satisfying \(a + b + c + d = 1\) . Prove that  
+
+\[(a + 2b + 3c + 4d)a^{a}b^{b}c^{c}d^{d}< 1.\]  
+
+By weighted AM- GM we have  
+
+\[a^{a}b^{b}c^{c}d^{d}\leq \sum_{\mathrm{cyc}}\frac{a}{a + b + c + d}\cdot a = a^{2} + b^{2} + c^{2} + d^{2}.\]  
+
+So, it is enough to prove that  
+
+\[(a^{2} + b^{2} + c^{2} + d^{2})(a + 2b + 3c + 4d)\leq 1 = (a + b + c + d)^{3}.\]  
+
+Expand both sides to get  
+
+\[+a^{3} + b^{2}a +c^{2}a +d^{2}a +a^{3} + 3b^{2}a +3c^{2}a +3d^{2}a\] \[+2a^{2}b +2b^{3} + 2bc^{2} + 2d^{2}b +3a^{2}b +b^{3} + 3bc^{2} + 3d^{2}b\] \[+3a^{2}c +3b^{2}c +3c^{3} + 3d^{2}c +3a^{2}c +3b^{2}c +c^{3} + 3d^{2}c\] \[+4a^{2}d +4b^{2}d +4c^{2}d +4d^{3} + 6abc +6bcd +6cda +6dab.\]  
+
+In other words, we need to prove that  
+
+\[+b^{3} + 2b^{2}a +2c^{2}a +2d^{2}a\] \[+a^{2}b +b c^{2} + d^{2}b\] \[+a^{2}d +b^{2}d +c^{2}d +3d^{3} + 6abc +6bcd +6cda +6dab\]  
+
+This follows since  
+
+\[2b^{2}a\geq b^{3} + b^{2}d\] \[2c^{2}a\geq 2c^{3}\] \[2d^{2}a\geq 2d^{3}\] \[a^{2}b\geq a^{2}d\] \[bc^{2}\geq c^{2}d\] \[d^{2}b\geq d^{3}\]  
+
+and \(6(abc + bcd + cda + dab) > 0\)  
+
+Remark. Some students complained this problem was "unfair" and they couldn't solve it because they didn't think an IMO problem would be solved only by expansion. I don't agree with this. Fedor Petrov provides the following motivational comments for why the existence of this solution should not be that surprising:  
+
+Better to think about mathematics. You have to bound from above a product \((a + 2b + 3c + 4d)(a^{2} + b^{2} + c^{2} + d^{2})\) , the coefficients \(1,2,3,4\) are increasing and so play on your side, so plausibly \((a + b + c + d)^{3}\) should majorize this term- wise, you check it and this appears to be true.
+
+
+
+He also gave the following advice:  
+
+The general advice is to study mathematics, not olympiad problems in past years. If the IMO problems set the students and their teachers on this path, I am more than satisfied.
+
+
+
+## \(\S 1.3\) IMO 2020/3, proposed by Milan Haiman (HUN), Carl Schildkraut (USA)  
+
+Available online at https://aops.com/community/p17821656.  
+
+## Problem statement  
+
+There are \(4n\) pebbles of weights \(1,2,3,\ldots ,4n\) . Each pebble is coloured in one of \(n\) colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two piles so the total weights of both piles are the same, and each pile contains two pebbles of each colour.  
+
+The first key idea is the deep fact that  
+
+\[1 + 4n = 2 + (4n - 1) = 3 + (4n - 2) = \dots .\]  
+
+So, place all four pebbles of the same colour in a box (hence \(n\) boxes). For each \(k = 1,2,\ldots ,2n\) we tape a piece of string between pebble \(k\) and \(4n + 1 - k\) . To solve the problem, it suffices to paint each string either blue or green such that each box has two blue strings and two green strings (where a string between two pebbles in the same box counts double).  
+
+![](data:image/jpeg;base64,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)
+  
+
+We can therefore rephrase the problem as follows, if we view boxes as vertices and strings as edges:
+
+
+
+Claim — Given a 4- regular multigraph on \(n\) vertices (where self- loops are allowed and have degree 2), one can color the edges blue and green such that each vertex has two blue and two green edges.  
+
+Proof. Each connected component of the graph can be decomposed into an Eulerian circuit, since 4 is even. A connected component with \(k\) vertices has \(2k\) edges in its Eulerian circuit, so we may color the edges in this circuit alternating green and blue. This may be checked to work. \(\square\)
+
+
+
+## \(\S 2\) Solutions to Day 2  
+
+## \(\S 2.1\) IMO 2020/4, proposed by Tejaswi Navilarekallu (IND)  
+
+Available online at https://aops.com/community/p17821585.  
+
+## Problem statement  
+
+There is an integer \(n > 1\) . There are \(n^2\) stations on a slope of a mountain, all at different altitudes. Each of two cable car companies, \(A\) and \(B\) , operates \(k\) cable cars; each cable car provides a transfer from one of the stations to a higher one (with no intermediate stops). The \(k\) cable cars of \(A\) have \(k\) different starting points and \(k\) different finishing points, and a cable car which starts higher also finishes higher. The same conditions hold for \(B\) . We say that two stations are linked by a company if one can start from the lower station and reach the higher one by using one or more cars of that company (no other movements between stations are allowed). Determine the smallest positive integer \(k\) for which one can guarantee that there are two stations that are linked by both companies.  
+
+Answer: \(k = n^2 - n + 1\)  
+
+When \(k = n^2 - n\) , the construction for \(n = 4\) is shown below which generalizes readily. (We draw \(A\) in red and \(B\) in blue.)  
+
+![](data:image/jpeg;base64,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)
+  
+
+To see this is sharp, view \(A\) and \(B\) as graphs whose connected components are paths (possibly with 0 edges; the direction of these edges is irrelevant). Now, if \(k = n^2 - n + 1\) it follows that \(A\) and \(B\) each have exactly \(n - 1\) connected components.  
+
+But in particular some component of \(A\) has at least \(n + 1\) vertices. This component has two vertices in the same component of \(B\) , as desired.  
+
+Remark. The main foothold for this problem is the hypothesis that the number of stations should be \(n^2\) rather than, say, \(n\) . This gives a big hint towards finding the construction which in turn shows how the bound can be computed.  
+
+On the other hand, the hypothesis that "a cable car which starts higher also finishes
+
+
+
+higher" appears to be superfluous.
+
+
+
+## \(\S 2.2\) IMO 2020/5, proposed by Oleg Kosik (EST)  
+
+Available online at https://aops.com/community/p17821528.  
+
+## Problem statement  
+
+A deck of \(n > 1\) cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards. For which \(n\) does it follow that the numbers on the cards are all equal?  
+
+The assertion is true for all \(n\) .  
+
+Setup (boilerplate). Suppose that \(a_{1},\ldots ,a_{n}\) satisfy the required properties but are not all equal. Let \(d = \gcd (a_{1},\ldots ,a_{n}) > 1\) then replace \(a_{1},\ldots ,a_{n}\) by \(\frac{a_{1}}{d},\ldots ,\frac{a_{n}}{d}\) . Hence without loss of generality we may assume  
+
+\[\gcd (a_{1},a_{2},\ldots ,a_{n}) = 1.\]  
+
+WLOG we also assume  
+
+\[a_{1}\geq a_{2}\geq \dots \geq a_{n}.\]  
+
+Main proof. As \(a_{1}\geq 2\) , let \(p\) be a prime divisor of \(a_{1}\) . Let \(k\) be smallest index such that \(p\nmid a_{k}\) (which must exist). In particular, note that \(a_{1}\neq a_{k}\) .  
+
+Consider the mean \(x = \frac{a_{1} + a_{k}}{2}\) ; by assumption, it equals some geometric mean, hence  
+
+\[\frac{n}{\sqrt[n]{a_{i_{1}}\cdot\cdot\cdot a_{i_{m}}}} = \frac{a_{1} + a_{k}}{2} >a_{k}.\]  
+
+Since the arithmetic mean is an integer not divisible by \(p\) , all the indices \(i_{1},i_{2},\ldots ,i_{m}\) must be at least \(k\) . But then the GM is at most \(a_{k}\) , contradiction.  
+
+Remark. A similar approach could be attempted by using the smallest numbers rather than the largest ones, but one must then handle the edge case \(a_{n} = 1\) separately since no prime divides 1.  
+
+Remark. Since \(\frac{27 + 9}{2} = 18 = \sqrt[3]{27\cdot 27\cdot 8}\) , it is not true that in general the AM of two largest different cards is not the GM of other numbers in the sequence (say the cards are \(27,27,9,8,\ldots)\) .
+
+
+
+## \(\S 2.3\) IMO 2020/6, proposed by Ting-Feng Lin, Hung-Hsun Hans Yu (TWN)  
+
+Available online at https://aops.com/community/p17821732.  
+
+## Problem statement  
+
+Consider an integer \(n > 1\) , and a set \(S\) of \(n\) points in the plane such that the distance between any two different points in \(S\) is at least 1. Prove there is a line \(\ell\) separating \(S\) such that the distance from any point of \(S\) to \(\ell\) is at least \(\Omega (n^{- 1 / 3})\) .  
+
+(A line \(\ell\) separates a set of points \(S\) if some segment joining two points in \(S\) crosses \(\ell\) .)  
+
+We present the official solution given by the Problem Selection Committee.  
+
+Let's suppose that among all projections of points in \(S\) onto some line \(m\) , the maximum possible distance between two consecutive projections is \(\delta\) . We will prove that \(\delta \geq \Omega (n^{- 1 / 3})\) , solving the problem.  
+
+We make the following the definitions:  
+
+- Define \(A\) and \(B\) as the two points farthest apart in \(S\) . This means that all points lie in the intersections of the circles centered at \(A\) and \(B\) with radius \(R = AB \geq 1\) .- We pick chord \(\overline{XY}\) of \(\odot (B)\) such that \(\overline{XY} \perp \overline{AB}\) and the distance from \(A\) to \(\overline{XY}\) is exactly \(\frac{1}{2}\) .- We denote by \(\mathcal{T}\) the smaller region bound by \(\odot (B)\) and chord \(\overline{XY}\) .  
+
+The figure is shown below with \(\mathcal{T}\) drawn in yellow, and points of \(S\) drawn in blue.  
+
+![](data:image/jpeg;base64,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)
+
+
+
+
+Claim (Length of \(AB + \text{Pythagorean theorem}\) ) — We have \(XY < 2\sqrt{nd}\) .  
+
+Proof. First, note that we have \(R = AB < (n - 1) \cdot \delta\) , since the \(n\) projections of points onto \(AB\) are spaced at most \(\delta\) apart. The Pythagorean theorem gives  
+
+\[XY = 2\sqrt{R^{2} - \left(R - \frac{1}{2}\right)^{2}} = 2\sqrt{R - \frac{1}{4}} < 2\sqrt{nd}.\]  
+
+Claim ( \(|T|\) lower bound + narrowness) — We have \(XY > \frac{\sqrt{3}}{2} \left(\frac{1}{2}\delta^{- 1} - 1\right)\) .  
+
+Proof. Because \(\mathcal{T}\) is so narrow (has width \(\frac{1}{2}\) only), the projections of points in \(\mathcal{T}\) onto line \(XY\) are spaced at least \(\frac{\sqrt{3}}{2}\) apart (more than just \(\delta\) ). This means  
+
+\[XY > \frac{\sqrt{3}}{2} (|T| - 1).\]  
+
+But projections of points in \(\mathcal{T}\) onto the segment of length \(\frac{1}{2}\) are spaced at most \(\delta\) apart, so apparently  
+
+\[|T| > \frac{1}{2} \cdot \delta^{-1}.\]  
+
+This implies the result.  
+
+Combining these two this implies \(\delta \geq \Omega (n^{- 1 / 3})\) as needed.  
+
+Remark. The constant \(1 / 3\) in the problem is actually optimal and cannot be improved; the constructions give an example showing \(\Theta (n^{- 1 / 3} \log n)\) .
+
+