Suppose that you're given a fair coin and you would like to simulate the probability distribution of repeatedly flipping a fair (six-sided) die. My initial idea is that we need to choose appropriate integers $k,m$, such that $2^k = 6m$. So after flipping the coin $k$ times, we map the number encoded by the k-length bitstring to outputs of the die by dividing the range $[0,2^k-1]$ into 6 intervals each of length $m$. However, this is not possible, since $2^k$ has two as its only prime factor but the prime factors of $6m$ include three. There should be some other simple way of doing this, right?