Problem A. 631. (December 2014)
A. 631. Let \(\displaystyle k\ge1\) and let \(\displaystyle I_1,\ldots,I_k\) be nondegenerate 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 12 January 2015.
Statistics:
3 students sent a solution.  
5 points:  Williams Kada. 
3 points:  1 student. 
0 point:  1 student. 
