No magic after all

We saw that knights can be very strong pieces on the chess board. But in this study we see that even four knights cannot win the game over a single sole bishop. The next study is a beautiful example, in the Netherlands known as "het traktor probleem", i.e. the tractor problem. The story goes that Tal saw this problem, looked at it for 10 minutes and then left for a walk. After he returned he showed the solution. It is still unclear who exactly composed the study, Harold van der Heijden devoded a few pages to it in ARVES 1995 4

It seems that black is totaly winning. But the question is "How can white win this postion?"

White's only trumph is the d7 pawn which can directly promote, but black has Nf7+ winning back the queen. White starts with 1. Nh5+ and black seems to have a small problem. If the King moves to the 8the rank the d-pawn promotes with check. The black King can also not move to h7 as after Lc2+  the King has to move to the 8th rank again. Obviously, Kf7 is blocking f7 for the knight. So the only move is 1.... Kg6

The only forcing move to whits disposal is now 2. Bc2+ Kxh5 Black has to take, there are no good alternatives

But whats next? If white promotes his pawn, again Nf7 is coming Checks with either the bishop or the pawn do not seem to work either.

3. d8Q!! Nf7+ 4. Ke6 Nxd8+ 5. Kf5

This is white's idea. He is threating mate again (Bd1+) and there is only one move to stop this

5... e2  but white is reinstalling the mate threat by 6. Be4

Again there is only one move, which stops the immediat mate threat Bf3+, it is the a Knight promotion

6.... e1N

White does not seems to have any forced moves left. Black is ready to promote his c-pawn by c3-c2-c1. To reinstall mate threats, the white Bishop has to reach the winning diagonals "d1-h5 or e8-h5". This cannot be done in one move. White plays the beautiful move 7. Bd5 

White will take 2 moves to return to the "winning diagonals" The threat is Bd5-c4-e2 and although this seems to be very slow, black has not that many moves left to defend. Both Knights on d8 and e1 are stucked (due to Bf7+ or Bf3+ checkmate) and the other four pieces do not seem to be able to guard the essential fields c4 or e2.

Black has one idea left, again related to a knight promotion

7.... c2 8. Bc4 c1N 

Four Knight should be enough to stop the bishop, should they?

well no! 9. Bb5 

Basically this is it. White has the immediat Be8+ but also the two-mover  Ba4-d1

Black plays 9.... Nc6 11. Bxc6 (this hold a bit longer compared to the immediat Nc7) 10..... Nc7 

11. Ba4  No escape for black, he can only sacrifise a few useless Knights, but that will not change anything 11.... Ne2 12. Bd1 Nf3

13 Bxe2 Ne6 15. Bxf3 check mate

So the Knights fairytale is over, there is no magic after all.



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