[Retros] Happy New Year!

[Juha Saukkola]

Do you have these already composed until 2050? Or more?


>From: Noam Elkies <elkies at math.harvard.edu>

>Reply-To: The Retrograde Analysis Mailing List <retros at janko.at>

>To: retros at janko.at

>Subject: Re: [Retros] Happy New Year!

>Date: Fri, 13 Jan 2006 12:20:29 -0500 (EST)

>

>Joost writes:

>

> > There are probably easier solutions, but here are mine:

>

>These look right, of course; The only improvement I can offer

>is that in the first problem:

>

>    +-----------------+

>    | . n b q . r k _ |   Noam D. Elkies, 12/2005

>    | _ p p p n p p p |

>    | . _ . _ r _ . _ |

>    | p . b . p . _ . |

>    | . _ . _ . P . _ |

>    | _ . _ P _ N _ . |

>    | P P P B P _ P P |   16+16

>    | R N K Q . B R . |   SPG-7.5: How many solutions?

>    |_________________|

>

>The count of 34 Black sequences can be obtained more easily

>by starting from  Binomial(7,3) = 35  -- the total number

>of ways to mathematically combine the three-move sequence

>a5, Ra6, Re6 and the four-move sequence e5, Bc5, Se7, O-O

>-- and substracting the one impossible combination

>a5, Ra6, Re6, e5, Bc5, Se7, O-O.

>

>In the second problem:

>

>    +-----------------+

>    | _ . _ . _ . _ . |   Noam D. Elkies, 12/2005

>    | . _ . _ . _ . _ |

>    | _ . _ . _ . _ . |

>    | . K . _ . _ . _ |

>    | _ . P . _ R _ P |

>    | . _ . _ . P . _ |

>    | P P Q P P . P . |   16+0

>    | R _ B N . B N _ |   OSPG-14: How many solutions?

>    |_________________|

>

>the factor of 2 due to the interchangeability of Qc2/Sc3

>applies throughout, so one could also count the total as

>2*[Binomial(14,4)+2].  Note that the four-move sequence

>had to keep the White King from reaching b5 in five moves

>via d1-c2.  It so happens that the Kb5/Pc4 device also

>appeared in my 2004-solution problem, where it was used

>to obtain the factor 167 as  Binomial(11,3) + 2.

>

>NDE

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