# 1/21/2011 - Knights Tour

• 2 years ago · Quote · #161

a bit too long, but I did it!

• 2 years ago · Quote · #162

It is very interesting! In this puzzle we work with only the knight all time.

• 2 years ago · Quote · #163

very drawn out, but nice

• 2 years ago · Quote · #164

finnaly!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!L!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

• 2 years ago · Quote · #165

nice long end game puzzle

• 2 years ago · Quote · #166
• 2 years ago · Quote · #167

pretty kewl

• 2 years ago · Quote · #168

i thought it to long....

• 2 years ago · Quote · #169

What a run, great one...

• 2 years ago · Quote · #170

oh my !

• 2 years ago · Quote · #171
elindauer wrote:

Amazing puzzle.  The key to solving it is to understand corresponding squares between the knight and the bishop.  Build up a set of them:

- Nd7#.  also Nxh7# so...

- if the knight gets to b8, b6, c5, e5, g5, or f6, it must be immediately captured by the bishop.  If not, white wins.

Now you can begin to build up corresponding squares.

- Nd3 threatens Nc5 and Ne5.  Black must play Bd4 or they lose.

- Nf3 threatens Ne5 and Nxg5.  Black must play Bf4 or Bf6(! Kxf6 stalemate)

You can take it another step back:

- Ne1 threatens Nd3 (forcing Bd4) and Nf3 (forcing Bf4 or f6). black must play Be3 or someplace on the a1-h8 diagonal (a1, b2, c3, g7, h8, but not d4 as Nd3 zugzwand!  also not Bf6 as Nf3 zugzwand!).

Until eventually you find that white is threatening enough squares that the black bishop has no defense.  You can build these up in pairs and cover the whole board.  Continuing on:

- Ne4 threatens Nxg5, Nf6 and Nc5, so Be7 is forced

- Nd2 threatens Ne4 (Be7) and Nf3 (Bf4, Bf6).  Bd8 is forced.

- Nc4 threatens Nd2 (Bd8), Ne5, and Nb6. Bc7 is forced.

- Nd6 threatens Nc4 (Bc7) and Ne4 (Be3 or Be7). Bd8 or Bb6 forced.

- Nb7 threatens Nd6 (Bd8 or Bb6) and Nc5.  Be7 or Bb6 forced.

- Na5 threatens Nb7 (Be7 or Bb6) and Nc4 (Bc7)...

... wait a minute!  The only dark square that can reach both c7 and (e7 or b6) is d8!  if the bishop were on d8, then of course we could not play Na5.  So that means a5 can be added as a winning square... if we ever reach this square, black must be ready to capture the knight immediately, or white wins!  ok, moving on:

- Nc6 threatens Na5 (win shown above), Ne5 and Nb8 (threat Nd7#).  Bc7 forced.  Notice that Bc7 is showing up often as a key defensive square...

- Nd4 threatens Nc6 (Bc7) and Nf3 (Bf4 or f6) and Kf6! opening up Ne6#.  Bd8 forced.

Now for the key moment... I've gone in a loop!  Now I can look back at Nf3, which reads:

- Nf3 threatens Ne5 and Nxg5.  Black must play Bf4 or Bf6(! Kxf6 stalemate)

and note that I have added another threat!
- Nf3 threatens Ne5, Nxg5 and Nd4 (Bd8).  So Bf6 is forced! I'm narrowing down the possibilities for the bishop.  Now back to Ne1...

- Ne1 threatens Nd3 (forcing Bd4) and Nf3 (forcing Bf4 or f6). black must play Be3 or someplace on the a1-h8 diagonal (a1, b2, c3, g7, h8, but not d4 as Nd3 zugzwand! also not Bf6 as Nf3 zugzwand!).

But no.  Now we know that Nf3 forces Bf6.  so the bishop must be on the a1-h8 diagonal.  Now finally, Nc2...
- Nc2 threatens Ne1 (a1, b2, c3, g7, h8) and Nd4 (Bd8). Ba5 forced.
and we have it!  The bishop starts on a3, so it cannot play Ba5 in response to Nc2.

To sum it all up:

Nice analysis of the strategy here.  But you must include the fact that to cover the necessary squares with the bishop, black must be willing to let the white knight capture the bishop.  In fact, he has no problem in letting that happen, because it results in a stalemate.  This is why his 11th move should have been to d4 (not to f3).

• 2 years ago · Quote · #172

SO long but SO good

• 2 years ago · Quote · #173

nice

• 2 years ago · Quote · #174

very nice!

• 2 years ago · Quote · #175
dufferps wrote:

Nice analysis of the strategy here.  But you must include the fact that to cover the necessary squares with the bishop, black must be willing to let the white knight capture the bishop.  In fact, he has no problem in letting that happen, because it results in a stalemate.  This is why his 11th move should have been to d4 (not to f3).

11... Bd4 12. Nxg5 and there is no defense to 13.Nxh7#.  This is why when the knight gets to f3, the corresponding square for the bishop is f6.  f4 fails as in the puzzle, all other locations fail immediately to either Ne5 or Nxg5.

• 2 years ago · Quote · #176

That was a pretty good puzzle, but I doubt that one would need to taunt the bishop for checkmate, it probably could have been won in just a few moves.

• 2 years ago · Quote · #177

I think honestly that it is a little long and there is a more efficient method

• 2 years ago · Quote · #178

great puzzle. I don't believe anyone solved this one. It just shows how powerful and unpredictable a knight can be in a BISHOP v KNIGHT endgame

• 2 years ago · Quote · #179
xMFNx wrote:

I think honestly that it is a little long and there is a more efficient method

show it

• 2 years ago · Quote · #180