In his post “A chess problem begging for a solution“, Michael Kaplan quotes Barbara Hambly’s Star Trek novel Ishmael. In the quoted scene, Spock (AKA Ishmael) plays a couple of chess games against a stranger – rather unusual chess games. The problem alluded to is to determine the moves of the games given certain information.

Let’s take the second game first. There are two effective possibilities that meet the “Reverse Fool’s mate” and “three moves” criteria:

Reverse Fool’s mate, even material: $200 in 2½ moves

# | Ishmael | Stranger |

1. | e3 | f6 |

2. | a3 | g5 |

3. | Qh5# |

… and…

Reverse Fool’s mate plus a pawn: $220 in 2½ moves

# | Ishmael | Stranger |

1. | e4 | f5 |

2. | exf5 | g5 |

3. | Qh5# |

The task for the first game, then, is to win either $400 or $380 in seven moves. Assuming the game ends in mate (this is reasonable) gives us a difference of either $200 or $180. The first move can not be a capture, so we really only have six moves to capture $200 worth of material – going after the queen is obvious, but the rooks are quite well tucked away, and it is hard to go after them and simultaneously set up the ending mate.

I believe that the solution that Barbara Hambly had in mind is the following variation of the “other” mate that every chess student learns (Scholar’s Mate). This particular setup is gated by White’s need to move his Bishop out of the way, and this nicely satisfies the common convention that players alternate colors in successive games. Naturally Spock, being a gentleman, would let the stranger take White first.

Mate, a queen, and four pawns: $380 in 7 moves

# | Stranger | Ishmael |

1. | c4 | e6 |

2. | c5 | Bxc5 |

3. | d4 | Bxd4 |

4. | e3 | Bxe3 |

5. | Qf3 | Qf6 |

6. | Bc4 | Qxf3 |

7. | Kf1 | Qxf2# |

However, from a “chess problem” point of view, there’s a cook. It is, in fact, possible to get mate plus a queen plus four pawns in a mere five and a half moves, rather than the seven full moves above:

Mate, a queen, and four pawns: $380 in 5½ moves

# | Ishmael | Stranger |

1. | e3 | h5 |

2. | Qxh5 | d5 |

3. | Qxd5 | Bf5 |

4. | Qxb7 | Bh7 |

5. | Qxc7 | Qc8 |

6. | Qxc8# |

Even worse, there is a way to get $400 in a mere *four and a half moves*.

Mate, a queen, a bishop, and a knight: $400 in 4½ moves

# | Ishmael | Stranger |

1. | d4 | Nh6 |

2. | Bxh6 | b7 |

3. | Qd3 | Ba6 |

4. | Qxa6 | Qc8 |

5. | Qxc8# |

The problem, as it stands, is therefore underdetermined… Spock and the stranger had a full two and a half moves to play around with in the first game, either to exchange material or perhaps to allow the stranger to pick up a free pawn (and return it in the second game.)