A chess problem begging for a solution...

by Michael S. Kaplan, published on 2009/04/08 10:01 -04:00, original URI: http://blogs.msdn.com/b/michkap/archive/2009/04/08/9537233.aspx


A regular reader gave me an interesting problem, from a book.

If that kind of puzzle is not your thing feel free to ignore....

Here is the text, from a book, that describes the setup for the problem:

    Behind them in the billiard room a man's voice grumbled, "Damn kid's game. Not a man's game in the place." The speaker intruded his wide shoulders between Ish and Joshua; a big man dressed in black clothing a bit too dandified for a rancher, a knight's head stickpin glinting in the dark silk of his cravat. The smell of whiskey hung faintly around him, but there was, too, an edge of danger, a readiness for trouble that said, Gunfighter.
    At the blackjack table, Jason leaned forward his red-and-gold waistcoat bright as blood against the white of his sleeves. He looked at his cards, leaned back, and folded.
    Behind them, the big mn grumbled, "About as much skill and thinking as Faro. Spit in the Ocean! Acey-Ducey Under-My-Shoosie! Doesn't anybody in this Godfersaken hell play chess?"
    Without so much as turning his head, Ishmael inquired, "At how much a piece?"
    Mate was set at two hundred dollars. Queen went for a hundred ("About the price of any woman in this town," remarked someone), rooks seventy-five, bishops and knights fifty. Pawns were twenty dollars a piece. A mystified owner scoured the surrounding saloons for a chess set and finally came up with one that the owner of Florinda's Place kept for decoration in her parlor.
    Ishmael beat the stranger in seven moves.
    "By God!" roared the big man. "Let me see you try that again, stranger!:
    He caught him with a reverse fool's mate, in three.
    "But that," he said, pocketing his cash, "is a classic fakement."
    The big man stroked his narrow black mustache and regarded his closed-in king thoughtfully through a haze of cigar smoke. Then he looked back up at Ish. "After I beat you this time," he said, "show me that one again."
    Warned, stung and $600 poorer, the gunfighter settled down to grim play...."

Things you should keep in mind:

The questions that you must answer to solve the problem:

  1. Is the $600 a true calculation based on two actual possible chess games?
  2. If the answer to #1 is yes, who was black and who was white in each game?
  3. If the answer to #1 is yes, what would be an exact sequences of moves in each game to cause the $600 cost of the two games?
  4. If the answer to #1 is yes, are there other potential sequences that could fit all of the known facts given in the problem?

It took me a bit longer to wok this one out than I would have liked, but I have been out of practice as I have not played chess in well over 15 years and have not played speed chess in almost half as long.

The prize?

I'll be very impressed if you solve the problem, even moreso if you beat my time, but most of all if you beat the time I feel I should have solved it in....

Ready? Set? Go!

 

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annoym on 13 Apr 2009 5:53 AM:

Fool's mate, also known as the "two-move checkmate," is the quickest possible checkmate in the game of chess. One example consists of the moves

1. f3 e5

2. g4 Qh4#

so,perhaps,the first game cost 400$ and the second cost 200$

akoltz on 15 Apr 2009 6:58 PM:

The answer to question #1 is "no."

I'm done, 3 seconds.

Did I win?

Maurits [MSFT] on 18 Apr 2009 12:07 AM:

Well, let's think this thing out.  The second game was a reverse fool's mate in three moves, which is quite a bit of information:

1) the game ended in mate.

2) since the shortest mate takes four half-moves, the term "moves" here refers to the standard chess meaning and not the colloquial "half-move" meaning.

3) the "reverse" implies that White won (Black wins the regular Fool's mate.)

4) Black has no time to capture anything.

5) White has time to capture at most one thing, and that would have to be a pawn.

So there are only a couple of possibilities for the second game.

-- GAME TWO, MATE PLUS A PAWN --

1. e4 f5?

2. exf5 g5??

3. Qh5# - white wins $220

or

-- GAME TWO, BLOODLESS MATE --

There are various different ways to do this.

1. e3 g5

2. Nc3 f6??

3. Qh5# - white wins $200

So we know Ishmael was White in the second game.  If the convention of alternating colors was followed, it's likely but not certain that Ishmael was Black in the first game.

We're given that the first game lasted seven moves, and that Ishmael's total net was $600; so he netted either $400 or $380 in the first game, depending on whether he got a pawn in the first game.

The word "beat" strongly suggests mate although the stranger could have resigned - both possibilities are worth exploring.

Exploring...

Maurits [MSFT] on 18 Apr 2009 1:12 AM:

The length of the first game is quite substantial.  There are sample games that work with a possible second game that are shorter than seven moves, so I suspect that there are multiple solutions.

To get $400, for example, one possibility is for Ishmael to get mate + queen + knight + bishop.  To get $380, one possibility is for Ishmael to get queen + knight + bishop and the stranger to get a pawn.

Sample game (with Ishmael as Black) taking only five moves, leaving two additional moves for fooling around.

1. Nh3 d5

2. b3 Qd6

3. Ba3 Qxa3

4. Qc1 Bxh3

5. Rg1 Qxc1#

Pair this with the bloodless mate and you have a solution.  Inject 1 ... g5 2. Nxg5 and pair it with the mate + a pawn and you have a different solution.

Maurits [MSFT] on 23 Apr 2009 11:21 PM:

There are also totally different possible first games involving Ishmael getting mate + queen + four pawns (the last moves being 7. Kf1 Qxf2#)

Maurits [MSFT] on 4 May 2009 8:30 PM:

Gory details here:

http://blogs.msdn.com/matthew_van_eerde/archive/2009/04/26/spock-s-chess-games-from-star-trek-ishmael.aspx

Michael S. Kaplan on 8 May 2009 10:16 PM:

After the solution given in

http://blogs.msdn.com/matthew_van_eerde/archive/2009/04/26/spock-s-chess-games-from-star-trek-ishmael.aspx

I'd say you get the job, though you already have it. So I guess that means you get to keep your job! :-)


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