# Benko's three-mover that stumped Fischer

In Christian Hesse's book The Joy of Chess one reads about a mate-in-3 problem composed by Pál Benkö that stumped Bobby Fischer. Hesse gives the following diagram:

``````[FEN "8/8/8/4k3/8/8/8/2BQKB2 w - - 0 1"]
``````

On the other hand, on ChessBase a slightly different diagram is given:

``````[FEN "8/8/8/8/4k3/8/8/2BQKB2 w - - 0 1"]
``````

Curiously, both of these positions are valid three-movers with the same key move! But which one is Benkö's actual composition?

You can find this chess problem

``````[FEN "8/8/8/8/4k3/8/8/2BQKB2 w - - 0 1"]
``````

on page 582 of Pal Benko's book "My Life, Games and Compositions" 2003 ISBN:1-890085-08-1 which also states it was first published in "Chess life" in 1968, so ChessBase is correct.

Given the hint of the same key move in both problems, I've systematically worked out all the various options for the solutions of both.

In the king on e4 problem, the solutions are:

1. Bc4 Ke5 2. Qd5+ Kf6 3. Qg5#. If 1. ... Kf5 2. Qf3+ Kg6 3. Qf7#. If 2... Ke5 in this line, 3. Qf4#. Alternately, 1... Kf5 2. Qh5+ Ke4 3. Qd5#. If 2... Kf6 in this line, 3. Qg5#

In the king on e5 problem, the solutions are:

1. Bc4 Ke4 2. Qd5# or 1... Kf5 2. Qh5+ Ke4 3. Qd5# or 1... Kf6 2. Qd6+ Kf5 3. Qe6# or finally, if 2... Kg7 in this latter line, 3. Qh6#.