4
Part of 2017 May Olympiad
Problems(2)
How many of them are divisible by $7$?
Source: May Olympiad 2017 level 2
7/24/2020
We consider all -digit numbers that are obtained by swapping in all ways Possible digits of . How many of them are divisible by ?
number theory
2 player game with red, bluec chips on n-gon 2017 May Olympiad L1 p4
Source:
8/25/2021
Let be an even integer greater than . On the vertices of a regular polygon with n sides we can place red or blue chips. Two players, and , play alternating turns of the next mode: each player, on their turn, chooses two vertices that have no tiles and places on one of them a red chip and in the other a blue chip. The goal of is to get three vertices consecutive with tiles of the same color. 's goal is to prevent this from happening. To the beginning of the game there are no tiles in any of the vertices. Show that regardless of who starts to play, Player can always achieve his goal.
gamecombinatoricswinning strategy