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Romania Team Selection Test
1998 Romania Team Selection Test
1998 Romania Team Selection Test
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Romania Team Selection Test
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Unit square grid not intersecting any segments in finite set
Consider in the plane a finite set of segments such that the sum of their lengths is less than
2
\sqrt{2}
2
. Prove that there exists an infinite unit square grid covering the plane such that the lines defining the grid do not intersect any of the segments.Vasile Pop
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parallelepiped
A parallelepiped has surface area 216 and volume 216. Show that it is a cube.