Puzzle of the week #13

Chess Diagram: 


Now we are back to one puzzle per week. The intro for it comes from Wikipedia (the free internet encyclopedia) and tells us in a few words who the Russian chess composer A. Troitsky was:
"Alexey Alexeyevich Troitsky, or Alexei, or Troitzky (March 14, 1866 - August ??, 1942) is considered to have been one of the greatest composers of chess endgame studies. He is widely regarded as the founder of the modern art of composing chess studies. (Seirawan 2003:91). He died of starvation during World War II at the siege of Leningrad, where his notes were destroyed. One of his most famous works involves analyzing the endgame with two knights versus a pawn, see Troitzky line. John Nunn analyzed this endgame with an endgame tablebase and stated that "the analysis of Troitsky ... is astonishingly accurate" (Nunn 1995:265)."
Each of Troitsky's chess compositions are of extreme beauty and of crystal clear chess logic. Great players separate themselves from the rest of us by being able to achieve unbelievable results with just a few pieces. Troitsky composed this endgame puzzle when he was 32 years old back in 1898. It is both beautiful and crystal clear in its simplicity. See diagram.
White to move and mate.
There are 2 possible lines, based on how Black responds: one is a mate in 3, the other one is a mate in 4. Each solution is worth 1 point. The answers will be published next week together with puzzle #14.

Both last week puzzles were excellent for practicing tactics during the spring break. Puzzle #12 also required keeping track of the many possible solutions, plus added the element of not knowing how many solutions were actually possible. An impressive number took the challenge very well and worked hard on puzzle #12. It is interesting to note how some found a few solutions of mate in 5, while others found only different ones.
Puzzle #11 solution:
Attacking Kf8 heads on is not good enough, as there are too many Black pieces in the way. White needs to find out the shortest route for Qe5 to deliver mate, while having the King help out; with the White King on "g6" the solution is kind of easy to spot now:
1.Qh2 Nf6 2.Qh8+ Ng8 3.Qxg7+ Ke8 4.Qxg8#
Correct solutions (perfect): Jacob, Jeremy, Karl, Joanne, Hanson, Algerd, Matthew, John D, Trevor, Katerina - 1.0 point
Puzzle #12 solution:
Normally a puzzle allowing multiple solutions of various number of moves is not very valuable. However in this case some mates were really nice; also I wanted to see how good the solvers are in keeping track of all solutions, as well as how creative they are! I will simply list all valid mates found and the names of those discovering them:
Mate in 3 - 1.Nxa7 Kxa7 2.Ne6 Kb6 3.Bc5# (Jacob, Frank, Karl, Jeremy, Matthew, Mark, Katerina, John D)
Mate in 4 - 1.Nxa7 Kxa7 2.Ka5 Ka8 3.a7 Kxa7 4.Kb5# (Jacob, Frank, Karl, Joanne, Matthew, Katerina, John D)
Mate in 5
1.Nxa7 Kxa7 2.Ka5 Ka8 3.Rb4 Ka7 4.Bb8+ Ka8 5.Bc6# (Karl, Joanne, Katerina)
1.Nxa7 Kxa7 2.Kb3 Ka8 3.Rb4 Ka7 4.Bb8+ Ka8 5.Bc6# (Joanne)
1.Nxa7 Kxa7 2.Kb5 Ka8 3.Re4 Ka7 4.Re7 Ka8 5. Bc6# (Jacob, Joanne, Trevor, Katerina, John D)
1.Nxa7 Kxa7 2.Ra5 Ka8 3.Rb5 Ka7 4.Bb8+ Ka8 5.Bc6# (Jacob, Jeremy, Matthew, Mark, Wilson, John D)
1.Nxa7 Kxa7 2.Bc8 Ka8 3.Nd7 Ka7 4.Bc5+ Ka8 5.Bb7# (Karl, Jeremy, John D)
1.Nxa7 Kxa7 2.Bc8 Kb6 3.Bb8 Kc6 4.Bb7+ Kb6 5.Nd7# (John D)
1.Nxa7 Kxa7 2.Bb5 Ka8 3.Nd7 Ka7 4.Bc5+ Ka8 5.Bc6# (Jacob)
1.Nxa7 Kxa7 2.Bb5 Kb6 3.Nd7+ Ka7 4.Bc5+ Ka8 5.Bc6# (Jacob)
1.Nxa7 Kxa7 2.Bc6 Kb6 3.Bb7 Ka7 4.Ne6 Kb6 5.Bc5# (Jeremy)
1.Nxa7 Kxa7 2.Ne6 Ka8 3.a7 Kb7 4.a8=Q+ Kb6 5.Qc6# (Jacob, Frank, Karl, Jeremy, Matthew, John D)
1.Nxa7 Kxa7 2.Ne6 Ka8 3.a7 Kb7 4.Kb5 Ka8 5.Bc6# (Jacob, Jeremy)
1.Nxa7 Kxa7 2.Ne6 Ka8 3.a7 Kb7 4.Nc5+ Kb6 5.Ra6# (Karl, Katerina)
1.Nxa7 Kxa7 2.Ne6 Ka8 3.a7 Kb7 4.Nc5+ Ka8 5.Bc6# (John D)
1.Nxa7 Kxa7 2.Ne6 Ka8 3.a7 Kb7 4.Nc5+ Kb6 5.a8=N# (John D)

Correct solutions (perfect)
John D - 12.0 points (4+8)
Jacob - 11.0 points (4+7)
Karl - 9.0 points (4+5)
Katerina - 8.0 points (4+4)
Joanne - 7.0 points (4+3)
Matthew - 7.0 points (4+3)
Frank - 6.0 points (4+2)
Jeremy - 6.0 points
Mark - 2.0 points
Trevor - 1.0 point
Wilson - 1.0 point

24.0 Jacob and John D
18.0 Karl and Jeremy
14.5 Joanne and Frank
13.5 Katerina
12.5 Matthew
11.0 Bryant
6.5 David
4.5 Algerd and Mark
3.5 Jakab
3.0 Karen and Trevor
2.5 Wilson
1.5 Nicholas
1.0 Jonah and Hanson
0.5 Alejandro, Vera, Kenneth and West