Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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.


Statistics:

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

Problems in Mathematics of KöMaL, December 2014