White to move and checkmate in 3.
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1.Rh8+ Kf7
2.Bg6+ Qxg6
3.Qe7# Success on first attempt. But there is another solution.
2.Re7+ Qxe7
3.Bg6#/Qg6#
I like to go by what has more variations. Therefore, I think that 1.Rh8+ is, in fact, the solution. Now, I haven’t had a lot of time to study varaitions because of my busy schedule, but things are calming down, and I intend at some point tonight or tomorrow go back and review as it is a good way to improve.
A puzzle is said to be perfect when the winning/drawing side for whom the puzzle is set has only one correct move at each step. This puzzle fails on that count.At the same time you have to admire the symmetry in both variations.1.Rh8+ is indispensable whereas white has a choice 2,Bg6+ or 2.Rg7+ on 2nd move. BQ captures in both cases.On 3rd move WQ can either dictate subordinates to do the job 3.Re7# / 3.bg6# or can deliver mate in person by 3.Qg6#/3.Qe7#. This symmetrical scheme is more beautiful.
The problem setter could have made it a single solution one by replacing WR at e1 by that on e4 and removing WP at d5. Then the solution would be
1.Rh8+ Kf7 2.Re7+ Qxe7 3.Qg6#
because 2.Bg6+ is impossible and 3.Bg6+ leaves escape square at e6 but I admit there will be no charm left.