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