Problem K. 484. (December 2015)

K. 484. Every natural number 1 to \(\displaystyle n\) is written on a card. What is the smallest \(\displaystyle n\) such that no matter how the cards are divided into two packs, there will always be two cards in one of the packs with two numbers that add up to a perfect square?

(6 pont)

Deadline expired on January 11, 2016.

Statistics:

76 students sent a solution.
6 points:	Barta Ákos, Bognár Ádám, Csóka Zoárd, Dékány Barnabás, Dobák Dániel, Farkas Norbert, Fekete Barnabás, Földvári Ádám, Gárdonyi Csilla Dóra, Gréczi Gergely Ádám, Hoffmann Balázs, Kárpáti Kristóf, Keltai Dóra, Kertész Ferenc, Kiss 468 Péter, Kiss 660 Anna, Kluèka Vivien, Kovács 161 Márton Soma, Kovács 439 Boldizsár, Kovács 576 Kristóf, Lénárt Martin, Magyar Gergely, Nagy Csaba Jenő, Nyitrai Boglárka, Pálvölgyi Szilveszter, Pinke Jakab Zoltán, Póta Balázs, Simon Dóra, Szántó Julianna, Varga 294 Ákos, Vida Kata, Zsótér Laura.
5 points:	Koleszár Panna, Kun-Szabó Anna, Miskolczi Abigél, Patkós Viktória, Ruzsa Kata, Tóth Benedek.
4 points:	7 students.
3 points:	5 students.
2 points:	1 student.
1 point:	17 students.
0 point:	8 students.

Problems in Mathematics of KöMaL, December 2015