MathDB

Derek the Dolphin and Kevin the Frog are playing a game where they take turns taking coins from a stack of

N

coins, except with one rule: The number of coins someone takes each turn must be a power of

6

. The person who cannot take any more coins loses. If Derek goes first, how many integers

N

from

1

6^{2021}

inclusive will guarantee him a win? (Example: If

N = 37

, then a possible sequence of turns is: Derek takes one coin, Kevin takes

36

coins, and Kevin wins.)

Problem Statement