Let \(N\) be a positive integer and let \(\lambda = (\lambda_1, \lambda_2, \ldots, \lambda_l)\) be a partition of \(N\) of length \(l\), i.e., \(\sum_{i=1}^{l}\lambda_i = N\) with parts \(\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_l \geq 1\). Define \(T(\lambda)\) as the partition of \(N\) with parts \(l\), \(\lambda_1 – 1, \lambda_2 – 1, \ldots, \lambda_l – 1\), ignoring any zeros that might occur. Starting with a partition \(\lambda\) of \(N\), we describe Bulgarian Solitaire by repeatedly applying the shift operation \(T\) to obtain the sequence of partitions
\[\lambda, T(\lambda), T^2(\lambda), \ldots\]
We say a partition \(\mathcal{A}\) of \(N\) is \(T\)-cyclic if \(T^i(\mu) = \mu\) for some \(i \geq 1\). Brandt \([2]\) characterized all \(T\)-cyclic partitions for Bulgarian Solitaire. In this paper, we give an inductive proof of Brandt’s result.