5
Problems(2)
2player game with 2019 coins (2019 Auckland MO J5)
Source:
11/14/2021
coins are on the table. Two students play the following game making alternating moves. The first player can in one move take the odd number of coins from to , the second player in one move can take an even number of coins from to . The player who can not make a move is lost. Who has the winning strategy in this game?
gamecombinatoricswinning strategy
coloring a map by 2019 circles (2019 Auckland MO S5)
Source:
11/15/2021
circles split a plane into a number of parts whose boundaries are arcs of those circles. How many colors are needed to color this geographic map if any two neighboring parts must be coloured with different colours?
Coloringcombinatoricscombinatorial geometry