MathDB
2019 plates in a circle with one cake in each, numbers from 1-16

Source: St. Petersburg 2019 9.7

May 2, 2019
combinatoricsgameminimumgame strategy

Problem Statement

In a circle there are 20192019 plates, on each lies one cake. Petya and Vasya are playing a game. In one move, Petya points at a cake and calls number from 11 to 1616, and Vasya moves the specified cake to the specified number of check clockwise or counterclockwise (Vasya chooses the direction each time). Petya wants at least some kk pastries to accumulate on one of the plates and Vasya wants to stop him. What is the largest kk Petya can succeed?