# Here you can find IMO problems since 1986 and complete results since 1992. Shortlisted problems can be found from Andrei Jorza's website and from IMO

ﬁnd, for several of the years, scanned versions of available original shortlist and longlist problems, which should give an illustration of the original state the IMO materials we used were in.

Let A1= 0.12345678910111213, A2= 0.14916253649, A3= 0.182764125216 , A4= 0.11681256625 , and so on. The decimal expansion of Anis obtained by writing out the nth powers of the integers one after the other. IMO Shortlist 1986 IMO ISL 1986 p 1 Let $A,B$ be adjacent vertices of a regular $n$-gon ($n\ge5$) with center $O$. A triangle $XYZ$, which is congruent to and initially coincides with $OAB$, moves in the plane in such a way that $Y$ and $Z$ each trace out the whole boundary of the polygon, with $X$ remaining inside the polygon. Find the locus of $X$.

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In 2010 and 2012, I submitted no problems. 1. MY PROBLEMS ON THE IMO EXAMS I1.IMO 2009 Problem 4 Let ABC be a triangle DONATE TO HURRICANE HARVEY RELIEF FUND https://www.redcross.org/donate/hurricane-harveyAOPS Link: https://artofproblemsolving.com/community/c6h60769p366557 IMO Shortlist 1991 1 Given a point P inside a triangle 4ABC. Let D, E, F be the orthogonal projections of the point P on the sides BC, CA, AB, respectively. Let the orthogonal projections of the point A on the lines BP and CP be M and N, respectively. Prove that the lines ME, NF, BC are concurrent.

## IMO SHORTLIST Number Theory 21 04N07 Let pbe an odd prime and na positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length pn. Prove that there exists a triangle with vertices at three of the given points such that the squares of its side lengths are integers divisible by

Show that |a| + |b| + |c| + |d| ≤ 7. 6.

### 27th IMO 1986 shortlisted problems. ------ A k-element subset is chosen at random from {1, 2, , 1986}. For which k is there an equal chance that the sum of

2.26. ASU 1986 . problems from around the world. Cao Minh Quang.

Contents: Meteor stream evolution – telescopic observations – meteor work in Sweden – meteor work in the U.K. – meteor work in Hungary – ZHR correction factors – very high meteor rates – Geminids 1985 – Perseids 1985 – large-format cameras – PMDB – prediction techniques – radio meteor work – quanta and
(only those not in IMO Shortlist) [3p per day] IMO TST under construction.

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Sign In. Details ﬁnd, for several of the years, scanned versions of available original shortlist and longlist problems, which should give an illustration of the original state the IMO materials we used were in. 2011 IMO Shortlist was also a joint work with Jan Vonk (Belgium). These two recent problems were submitted by Belgium. However, the other 16 problems were entirely my work, and thus submitted by Republic of Korea (South Korea). In 2010 and 2012, I submitted no problems.

27th IMO 1986 shortlisted problems. 7.

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### DONATE TO HURRICANE HARVEY RELIEF FUND https://www.redcross.org/donate/hurricane-harveyAOPS Link: https://artofproblemsolving.com/community/c6h60769p366557

IN THE NAME OF ALLAH IMO ShortList Problems 1959 – 2009 Collected by: 21 1981 75 19 1982 78 20 1983 81 25 1984 84 20 1985 87 22 1986 90 21 1987 Sep 3, 2019 The other novels on the shortlist announced in London on Tuesday include Obioma, born in 1986, is a Nigerian writer and assistant professor of Imo Police debunk House of Assembly attack, but confirm robbery in Ower Later in 1986, the Pan African Mathematics Olympiad commission was established Enhancement of the participation of African countries to PAMO and to IMO. participation of our team at the International Mathematical Olympiad (IMO). 1986. Warsaw. 5.

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### 1986: English: 1985: English: 1984: English: 1983: English: 1982: English: 1981: English: 1979

5.