Three Pawns Problem

The problem of a king opposed to three united passed pawns was examined as early as 1617 by Pietro Carrera, but was first solved by József Szén in 1836.* Knowing the solution is the key to solving this endgame position.

White to move

A few years ago, I had the opportunity to look at an article that Szén wrote on the subject. I could not read the text as it was in Hungarian, but the analysis was a form of algebraic notation and there were diagrams. I also have spent many hours playing these positions against the computer (see "Pawn Wars" [October 2009]).

This morning, I played the diagram against Stockfish after someone posted the position on Facebook.

Stockfish 6 64 -- Stripes,James
Spokane, 23.05.2015

1.h4 Kf8

Black begins with a waiting game.

2.g3 Kg8 3.h5

Now, Black must move to the seventh rank.

3...Kg7 4.f4 Kh7 5.f5

Black to move

This position is critical for Black

5...Kg8

Only move. Black is able to occupy any of the three critical squares on the seventh rank, depending upon which pawn White moves.

6.g4

6.h6 Kh7 7.f6 Kxh6

6...Kg7 7.g5 Kg8

Only move.

White to move

 8.f6 Kf7 9.h6 Kg6

White to move

This position was one of the keys Szen discussed in the article that he wrote about the three pawns problem. It should be clear that White is in zugzwang.

10.f7

10.h7 Kxh7

10...Kxf7 11.h7 Kg7 12.g6 Kh8

White to move

Playing against Stockfish often means playing until checkmate.

13.Ka2

13.g7+ Kxg7 14.h8Q+ Kxh8 15.Ka2 c2

13...c2 14.Kxa3 c1Q+ 15.Kb4 Qb1+ 16.Kc3 Qxg6 17.Kd4 Kxh7 18.Kd5 Qc2 19.Kd4 Kg6 20.Kd5 Qc3 21.Kd6 Qc4 22.Ke5 Qd3 23.Ke6 Qd4 24.Ke7 Qd5 25.Ke8 Kf6 26.Kf8 Qa8# 0–1

*David Hooper and Kenneth Whyld, The Oxford Companion to Chess (1996), 420.