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In the last diagram, black has Qxc3 to thwart white's plan. That's why it was necessary to take with the bishop in the previous diagram.
Collections are good one indeed.
Yeah I know, that's why it's in there! That Last one is titled what not to do. Thanks for looking though Loomis. The trouble is, when you put diagrams in, they sort of overlap the titles.
Oh, I got as far as "2. Qxf6 Can you see black's next?" and didn't realize the diagram contained another move. I thought we were supposed to answer.
Good collection!I found another way to checkmate in the 1st diagram: 3. Qh8+ Kf8 4. Qxg7#.
Kingskiller wrote: I found another way to checkmate in the 1st diagram: 3. Qh8+ Kf8 4. Qxg7#.
After 3. Qh8+, Kf8 is not a legal move.
Loomis wrote: Kingskiller wrote: I found another way to checkmate in the 1st diagram: 3. Qh8+ Kf8 4. Qxg7#.
After 3. Qh8+, Kf8 is not a legal move.
Correct, Loomis. I think it is good that it's the type of position that hasn't got one absolutely forcing line, so you have to soak the piece placement up and work things out in your head. Anyone who is thinking about ideas like kingskiller is on the right track, and its worth seeing why that isn't quite right so that you don't do it in a game. These sort of problems improve your tactical vision no end
Yes, Kingskiller obviously meant 3. Qh7+. This was the first mate I saw, and was bummed when the puzzle would not let me do it. I realized that Qh8+ was also mate just after, but a good puzzle has only one solution.
tonightonly7 wrote: Yes, Kingskiller obviously meant 3. Qh7+. This was the first mate I saw, and was bummed when the puzzle would not let me do it. I realized that Qh8+ was also mate just after, but a good puzzle has only one solution.
Agreed, but its not actually a puzzle, as in a study problem. It's from a real game. If you look, Black could also block the h-file with his Q on move 2. when white exchanges Queens and mates on h8. The tricky line to see is given in the notes to diagram 3. I.e. 1...Kb1 2. Bb4+ etc when black loses the Queen to a knight fork giving double check. For me, its these lines that can be missed and if you havent got a saving fork in your own game, you could lose.
tonightonly7 wrote: Yes, Kingskiller obviously meant 3. Qh7+. This was the first mate I saw, and was bummed when the puzzle would not let me do it. I realized that Qh8+ was also mate just after, but a good puzzle has only one solution.
Thank you, you're right that's what I wanted to say. Sometimes mistyping is my big problem - I'm typing too fast! 
In this, white is to play and win.
What I like about it is that black can try and wriggle out desperately, but still loses material if mate is avoided.
The mate itself is very instructive, because its not just the idea, but the move order that counts.
I will put the main variations in seperate diagrams rather than footnotes, for easy viewing.
This is a really good problem and worth investing some time in before looking at the answer. ENJOY!