Kvant Math Problem 2875
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Verified: no
Verdicts: UNKNOWN + UNKNOWN
Solve time: 13m42s
Source on kvant.digital
Problem
Petya chooses 100000 numbers from the interval $[1;1000]$. Vasya wants to take $3k$ of them and divide them into $k$ triples so that for each triple there exists a triangle whose side lengths are equal to the numbers in that triple. What is the largest $k$ for which Vasya can do this regardless of Petya's actions?
P. Kozhevnikov
Southern Mathematical Tournament (XX)
Working