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These two puzzles were actually recently published in the Problemist, a British chess problem journal. The first is a mate in three, the second a mate in four. Nowadays "direct mate" problems such as these are almost considered old-fashioned, but to people new to solving I think they still present something of a hopefully enjoyable challenge.
White to Play and Mate in Three
Very nice puzzles, evil rook moves for the dark squares. I saw a mate in 5 in the first one with 1.Ba7+ Bd4 2. Qf3+ gxf3 3. Rf3+ Kd2 4.Nxf3+ Kd1 5.Rc1#. I saw Rd7 and Qf1 in the second one, but was not thinking f4!!.
Is the cat rated? He (she?) could probably solve these puzzles faster than I could
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