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Geometry Shortlist Problem in IMO 2015

Problem 1. Let ABC be an acute triangle with orthocenter H. Let G be the point such that the quadrilateral ABGH is a parallelogram. Let I be the point on the line GH such that AC bisects HI. Suppose...

Combinatorics : Shortlist problem of IMO 2014

Problem 1: Let n points be given inside a rectangle R such that no two of them lie on a line parallel to one of the sides of R. The rectangle R is to be dissected into smaller rectangles...

Combinatorics Problem in Shortlist IMO problem 2015

Problem 1: In Line land there are towns, arranged along a road running from left to right. Each town has a left bulldozer (put to the left of the town and facing left) and a right bulldozer (put to...

Solving Domino’s problem for determine the smallest positive integer (Solution number 8 of shortlist combinatoric in IMO 2016)

Problem Combinatoric 8: Let n be a positive integer. Determine the smallest positive integer k with the following property: it is possible to mark k cells on a 2n x 2n board so that there exists a unique partition...

Solving segment problem in line and point ( Solution number 7 shortlist problem of combinatoric in IMO 2016)

Problem Combinatoric 7: Let be an integer. In the plane, there are n segments given in such a way that any two segments have an intersection point in the interior, and no three segments intersect at a single point....

Solve the route problem (solution number 6 Shortlist problem in IMO 2016 about combinatoric )

Problem Combinatoric 6: There are islands in a city. Initially, the ferry company offers some routes between some pairs of islands so that it is impossible to divide the islands into two groups such that no two islands in...

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