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on July 21, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 3
Let \(P = A_1, A_2 \dots A_k\) be a convex polygon on the plane. The vertices \(P = A_1, A_2 \dots A_k\) have integral coordinates and lie on a circle. Let \(S\) be the area of \(P\). An odd positive …
on June 6, 2014 | Updated Jan. 4, 2018
A constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular hepta…
on June 28, 2012 | Updated Dec. 6, 2017
A large rectangle is partitioned into smaller rectangles, each of which has either integer height or integer width or both. Prove that the large rectangle also has this property.
on May 7, 2014 | Updated Jan. 4, 2018
Quarter past three
How many degrees are there in the angle between the hour and minute of a clock when the time is a quarter past three ?
on June 16, 2013 | Updated Jan. 4, 2018
Let \(P\) be a polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points. Let \(I\) be the number of lattice …
on June 21, 2012 | Updated Dec. 6, 2017
A well known triangle
Let \(ABC\) be an acute-angled triangle. Find points \(X, Y, Z\) on sides \(BC, CA\) and \(AB\) such that the perimeter of the triangle \(XYZ\) is minimized.
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