Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4803. (May 2016)

B. 4803. Is it possible to specify closed intervals of rational endpoints on the number line such that every rational number is the endpoint of exactly one interval, and

$\displaystyle a)$ one of any pair of closed intervals contains the other;

$\displaystyle b)$ no pair of two intervals are disjoint, but no interval contains another?

Based on an idea of M. E. Gáspár

(6 pont)

Deadline expired on June 10, 2016.

### Statistics:

 52 students sent a solution. 6 points: Andó Angelika, Baran Zsuzsanna, Borbényi Márton, Bukva Balázs, Gáspár Attila, Hansel Soma, Imolay András, Janzer Orsolya Lili, Kerekes Anna, Keresztfalvi Bálint, Klász Viktória, Kovács 246 Benedek, Kőrösi Ákos, Lajkó Kálmán, Lakatos Ádám, Matolcsi Dávid, Molnár-Sáska Zoltán, Nagy Nándor, Németh 123 Balázs, Tóth Viktor, Váli Benedek, Várkonyi Dorka, Zólomy Kristóf. 5 points: Busa 423 Máté, Nagy Kartal, Saár Patrik, Varga-Umbrich Eszter. 4 points: 1 student. 3 points: 1 student. 2 points: 11 students. 1 point: 4 students. 0 point: 6 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, May 2016