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Here's our first checkmate! In the first example, black has no defense for his king along the back rank. White can move the rook forward all the way until it attacks the black king. Black cannot move his king, capture the rook, or place a piece between the king and the attacking rook. It's checkmate!
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In the second example, white shows off the power of doubled rooks. Here, black has a rook defending the back rank, but white has TWO attackers. As we learned early in life, two is better than one. White therefore moves the first rook all the way until it attacks the king. Black must capture the first rook, but white delivers the checkmate with the second rook!