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.

### 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