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Part of 2022 Tuymaada Olympiad
Problems(2)
Tuymaada 2022 junior P1
Source: Tuymaada 2022 junior P1
7/3/2022
Arnim and Brentano have a little vase with candies on the table and a huge sack with spare candies under the table. They play a game taking turns, Arnim begins . At each move a player can either eat candies or take candies from under the table and add them to the vase. A player cannot go under the table in two consecutive moves. A player is declared the winner if he leaves the vase empty. In any other case, if a player cannot make a move in his turn, the game is declared a tie. Is there a winning strategy for one of the players?
combinatorics
tuymaada P1 Senior
Source: tuymaada 2022 senior P1
7/3/2022
Some of towns of a kingdom are connected by roads.It is known that for each two towns and connected by a road there is a town which is not connected by a road with at least one of the towns and . Determine the maximum possible number of roads in the kingdom.
graph theory