Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 631. (December 2014)

A. 631. Let \(\displaystyle k\ge1\) and let \(\displaystyle I_1,\ldots,I_k\) be non-degenerate subintervals of the interval \(\displaystyle [0, 1]\). Prove \(\displaystyle \sum \frac1{|I_i\cup I_j|} \ge k^2\) where the summation is over all pairs \(\displaystyle (i,j)\) of indices such that \(\displaystyle I_i\) and \(\displaystyle I_j\) are not disjoint.

Miklós Schweitzer competition, 2014

(5 pont)

Deadline expired on January 12, 2015.


3 students sent a solution.
5 points:Williams Kada.
3 points:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, December 2014