Question: Let n be a positive integer and let Bra be the 'triangular' chessboard with left-justified rows consisting of n - 1, n - 2 .

Let n be a positive integer and let Bra be the 'triangular' chessboard with left-justified rows consisting of n - 1, n - 2 . . . 1 squares from top to bottom. The board B6 is shown below, with three non-attacking rooks. Prove that the number of ways to place r non-attacking rooks on El. equals the number of set partitions of [n] with n - r blocks.

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