Say I have a one bit random variable $X \in \{0,1\}$, and let $n$ be a natural number. I want a sequence of random variables $0 = X_0, X_1, \ldots, X_n = X$ s.t.
$$H\left(X~|~\{X_0,\ldots,X_k\}\right) = 1-\frac{k}{n}$$
That is, each additional $X_k$ provides $1/n$ of the information of $X$, until everything is revealed by $X_n = X$. Is there a nice construction for this sequence?