Message #1946

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: new {5,4} puzzles
Date: Sat, 03 Dec 2011 12:56:39 -0600

Hi Andrey,

Can your technique be used to find non-orientable paintings? Maybe there
is a way to have the F_25 field give the 12-color {5,4} and a corresponding
{5,3,4} with much less than 130 colors?

In any case, I do still think VT, ET, and RT versions of a 2-color {5,3,4}
would be worthy and enjoyable puzzles.

Roice

On Fri, Dec 2, 2011 at 2:18 PM, Andrey <andreyastrelin@yahoo.com> wrote:

> Hi Roice,
> Something was wrong in my mathematics. Now my calculations give different
> result:
>
> Field F_25 gives 24-color {5,4} and 130-color {5,3,4}
> Field F_81 gives 72-color {5,4} and 4428-color {5,3,4}
> Field Z_11 gives 264-color {5,4}
> Field Z_19 gives 1368-color {5,4}
> Field Z_29 gives 406 colors for both {5,4} and {5,3,4}
>
> So probably there is no good puzzles in {5,3,4}. Only hope is that thee
> will be good subgroup of 26 elements for F_25 or 29 or 58 elements for Z_29.
>
> Andrey