MathDB
2014 Advanced #7

Source:

July 1, 2022
2014Advanced Topics Test

Problem Statement

Two math students play a game with kk sticks. Alternating turns, each one chooses a number from the set {1,3,4}\{1,3,4\} and removes exactly that number of sticks from the pile (so if the pile only has 22 sticks remaining the next player must take 11). The winner is the player who takes the last stick. For 1k1001\leq k\leq100, determine the number of cases in which the first player can guarantee that he will win.