# [Retros] Happy New Year!

Juha Saukkola juha_saukkola at hotmail.com
Sat Jan 14 03:44:23 EST 2006

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

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

>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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