Mathematical and Physical Journal
for High Schools
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Problem A. 510. (May 2010)

A. 510. There is given a positive integer n and some straight lines in the plane such that none of the lines passes through (0,0), and every lattice point (a,b), where 0\lea,b\len are integers and a+b>0, is contained by at least a+b+1 of the lines. Prove that the number of the lines is at least n(n+3).

(5 pont)

Deadline expired on June 10, 2010.


4 students sent a solution.
5 points:Backhausz Tibor, Nagy 235 János, Nagy 648 Donát.
2 points:1 student.

Problems in Mathematics of KöMaL, May 2010