Moderator Note: At the time that this question was posted, it was from an ongoing contest. The relevant deadline has now passed.
Suppose that I flip a coin $t$ times. How can I find a generalized formula for the probability that the number of tails I will get will be equivalent to $0$ mod $3$ ?
I have tried my hand at this problem- I believe that the result is related to $t$ mod $6$. I am not able to get a formula that works, other than that.