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Too long. Solved all eight, but the brain cells don’t work so quickly anymore.
The first four are fairly easy:
#13:
1. Qc5+ Kd7
2. Qd6+ Ke8
3. Qe7#
#14:
1. Qxf8+ Kxf8
2. Nf6+ Kg8
3. Rf8#
#15:
1. Rh8+ Kxh8
2. Qxh6+ Kg8
3. Qxg7#
#16:
1. d6+ Ke6
2. Re8+ Kd5
3. Bb7+ Kc4
4. Rb4#
Now let me look at the remaining four. 🙂
13)
1. Qc5+ Kd7
2. Qd6+ Ke8
3. Qe7#
14)
1. Qf8+ Kxf8
2. Ng6++ Kg8
3. Rf8#
Took only the time to write the solution. But the rest is harder:
15)
1. Rh8+ Kxh8
2. Qxh6+! Kg8 (g7 was pinned)
3. Qxg7#
Took me a minute to find the right move order here (tried all other sequences first).
16)
1. d6+ Ke6
2. Re8+ Kd5
3. Rd1+ Kc6
4. Rc8#
Easy, since there were so few squares black king could walk on.
But took a minute though.
17)
1. Qc6+ Ka5
2. b4+ (magnetism) Kxb4
3. Qc5+ Ka4
4. Bd1#
Again, a minute.
18)
1. Kg4+ Kg6
2. Kf4+ Kf6
3. e5+ Ke6
4. Nc5#
Here I first tried 3. Bc3+? that didn’t work…
19)
Here is something tricky about the d7/d6 escape fields.
1. Re8+ Bxe8
2. Rxe8+ Kd7
3. Nf6+! Kxd6
4. Re6#
Not really difficult, but still took me 2 minutes.
20)
The last one seems surprisingly easy:
1. Nf6+ gxf6
2. Qg3+ Kf8
3. Bh6#
Well, black can prolong this with the interposing sack:
2. … Qg5
3. Qxg5+(?) Kf8
Oops, where is my mate in 4 now? My own queen suddenly stands in the way for my bishop!
Improvement:
1. Nf6+ gxf6
2. Qg3+ Qg5
3. Re8+! Kg7
4. Qxg5#
There had to be some fun in one of those puzzles:-)
Solutions for second set of four problems.
#17:
1. Qc6+ Ka5
2. b4+ Kxb4
3. Qc5+ Ka4
4. Bd1#
#18:
1. Kg4+!! Kg6
2. Kf4+ Kf6
3. e5+ Ke6
4. Nc5#
#19:
1. Re8+ Bxe8
2. Rxe8+ Kd7
3. Nf6+ Kxd6
4. Bf4#
#20:
1. Nf6+ gxf6
2. Qf8+ Kxf8
3. Bh6+ Kg8
4. Re8#
These are too hard.
@pht:
Your and my solutions differ in 3 cases (apart from a typo I made in #14):
1. #16
Your solution is wrong, since you missed the interposing move, 3… Rd3 after which there is no mate in 4.
2. #19
Both our solutions appear to work (the difference is only in the mating move)
3. #20
Your fourth move is not really a mating move, since you missed the pawn on f6. So, black escapes your purported mate with 4… fxg5. My solution is correct, though.
Comparing MrB’s solutions to my own, I can see my mistake on #16:
My solution is mate in 5, I overlooked blacks sack 3. … Rd3
I can also see my mistake on #20:
My solution is mate in 5, I overlooked blacks extra sack 2. … Bg4
About #19, are here three mates?
4. Re6#, 4. Bf4# or 4. Bf8#