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1. Qxe6+ Kxe6
2. Ng5+ Kd6
3. c5#
1 minute and 30 seconds
Again, less than 30 seconds, though once I spotted Qxe6, less than five after that.
1. Ng5 + Kg8
2.Qxe6+Kh8
3.Nf7 #
less than 1 min
Here is a cute little problem:
k7/8/PP6/K7/4p3/2Rp4/2r5/8 w – – 0 1
Thanks for the problem. I saw the idea at once.Here is the solution:
1. b7+ Ka7
2. Rc8 Ra2+
3. Kb4 Kxa6
4. b8=Q Rb2+
5. Kc3 Rxb8
6. Rxb8 Ka5
7. Kd2 Ka4
8. Ke3 Ka3
9. Kxe4 d2
10. Rd8 Kb4
11. Rxd2
Isn’t 1. Rc8+ R:c8 2. b7+ Kb8 3. Kb6 better? Black is forced to play 3….Rc6+ to avoid mate on the next move, and then it’s a simple matter to promote the b-pawn after 4. K:c6 Ka7 5. Kc7.
Your solution is better than mine.
1. Ng5+ Kg8 (forced)
2. Q:e6+ Kh8 (forced)
3. Nf7#
A dual!
Negative – after 3. Nf7+ Black still has 3…Kg8.