Problem A. 926. (February 2026)

A. 926. Let

\(\displaystyle A=\{[\frac{3+\sqrt{5}}{2}\cdot n]\colon n=1,2,3,\ldots\}=\{2,5,7,10,13,15,\ldots\}.\)

Two players, First and Second, play a game with a pile of \(\displaystyle N\) coins according to the following rules. The players move alternately, with First moving first. On each move, the player on turn chooses a number \(\displaystyle k\in A\) and removes \(\displaystyle k\) coins from the pile. A player who is unable to make a legal move loses the game. Determine, in terms of \(\displaystyle N\), which player has a winning strategy, and describe such a winning strategy.

Proposed by Attila Sztranyák, Budapest

(7 pont)

Deadline expired on March 10, 2026.

Statistics:

21 students sent a solution.
7 points:	Ali Richárd, Bodor Mátyás, Bolla Donát Andor, Forrai Boldizsár, Li Mingdao, Morvai Várkony Albert, Sárdinecz Dóra, Vigh 279 Zalán, Xiaoyi Mo	(9 students).
4 points:	2 students.
3 points:	2 students.
2 points:	3 students.
1 point:	3 students.
0 points:	2 students.

Problems in Mathematics of KöMaL, February 2026