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Part of 2011 Iran MO (2nd Round)
Problems(2)
points with distance at least 10 meters
Source: Iran second round 2011
4/28/2011
We have a line and points around it such that the distance of each point to the line is less than centimeters and the distance between any two points is more than centimeters. prove that there are two points such that their distance is at least meters ( centimeters).
geometryanalytic geometrycombinatorics proposedcombinatorics
smallest integer n with n numbers in (-1,1)
Source: Iran second round 2011
4/29/2011
find the smallest natural number such that there exists real numbers in the interval such that their sum equals zero and the sum of their squares equals .
algebra proposedalgebra