Re: Aufgabe::Rechteckige Matrizen

["Udo und Susanne Krause" <su.krause@XXXXXXX.ch>]

Hallo Robert,

> nach Bildung der Pseudoinversen erhält man mit den von Null
> verschiedenen Elementen die Lottozahlen für den
> 21. Dezember, nur leider ...

wissen Sie nicht, bei welcher Lottogesellschaft und, schlimmer noch,
ob o.g. Lotto-Eigenschaft auch für diese Matrix

{{1, 20, 4, 10, 6, 9, 2, 12, 5, 11, 15, 19, 17, 3, 8, 7, 13, 14, 16, 18},
 {2, 1, 20, 4, 10, 14, 5, 3, 11, 6, 16, 9, 12, 8, 7, 13, 15, 17, 18, 19},
 {4, 2, 1, 15, 6, 14, 5, 10, 9, 8, 13, 12, 18, 7, 11, 16, 17, 19, 20, 3},
 {5, 3, 2, 1, 4, 9, 16, 15, 6, 10, 12, 8, 13, 14, 7, 11, 17, 18, 19, 20},
 {9, 3, 2, 16, 6, 17, 5, 15, 12, 13, 10, 11, 14, 7, 18, 19, 8, 20, 4, 1},
 {13, 18, 3, 9, 17, 15, 7, 8, 6, 16, 14, 19, 20, 10, 11, 2, 12, 1, 5, 4},
 {16, 17, 15, 14, 10, 7, 9, 12, 5, 6, 11, 8, 13, 18, 19, 3, 20, 1, 4, 2},
 {17, 15, 6, 16, 14, 9, 12, 4, 10, 13, 11, 5, 18, 19, 20, 7, 1, 2, 3, 8},
 {19, 7, 20, 17, 15, 16, 13, 2, 6, 14, 18, 8, 9, 10, 4, 1, 5, 11, 3, 12},
 {18, 11, 15, 1, 20, 19, 13, 9, 14, 17, 7, 2, 6, 8, 3, 4, 5, 10, 12, 16},
 {20, 19, 10, 18, 14, 5, 16, 8, 13, 15, 1, 9, 6, 3, 2, 7, 4, 11, 12, 17}}

zutrifft; die gesuchten Eigenschaften hat sie natürlich.

Gruss
Udo.

> On 06.12.2012 06:31, Udo und Susanne Krause wrote:
> > Hallo,
> >
> > hier sind drei weitere Matrizen dieser Art, die Frage bleibt: welcher
> > Art?
> >
> >
> > {{1, 18, 17, 16, 9, 3, 5, 2, 4, 7, 6, 10, 15, 13, 12, 14, 8, 11},
> >  {2, 1, 18, 17, 16, 11, 14, 4, 6, 3, 5, 7, 10, 9, 8, 12, 13, 15},
> >  {4, 2, 1, 18, 17, 16, 9, 13, 5, 8, 6, 12, 7, 15, 11, 10, 14, 3},
> >  {5, 3, 2, 1, 18, 4, 17, 16, 15, 14, 8, 7, 6, 13, 11, 9, 12, 10},
> >  {9, 3, 2, 8, 18, 7, 6, 17, 16, 5, 15, 14, 4, 10, 13, 11, 12, 1},
> >  {13, 18, 12, 17, 16, 11, 15, 6, 7, 10, 3, 8, 5, 1, 9, 14, 4, 2},
> >  {15, 5, 6, 1, 14, 18, 13, 12, 17, 11, 10, 8, 16, 7, 2, 9, 3, 4},
> >  {16, 7, 1, 6, 15, 18, 14, 17, 13, 12, 8, 10, 2, 9, 11, 3, 4, 5},
> >  {17, 11, 4, 2, 3, 7, 5, 6, 1, 12, 10, 18, 9, 16, 14, 15, 13, 8},
> >  {18, 17, 4, 7, 2, 3, 6, 5, 11, 1, 16, 10, 9, 8, 15, 13, 12, 14}}
> >
> >
> >
> > {{1, 16, 7, 4, 6, 3, 2, 11, 10, 5, 9, 8, 13, 12, 14, 15},
> >  {2, 1, 15, 14, 12, 7, 6, 5, 4, 3, 10, 8, 9, 13, 11, 16},
> >  {4, 2, 1, 16, 15, 14, 11, 13, 7, 5, 6, 9, 10, 12, 8, 3},
> >  {5, 3, 2, 1, 16, 15, 4, 13, 14, 11, 6, 8, 7, 10, 9, 12},
> >  {9, 3, 8, 2, 7, 6, 5, 15, 16, 4, 10, 14, 13, 11, 12, 1},
> >  {13, 12, 16, 15, 11, 10, 9, 6, 5, 4, 7, 8, 14, 1, 3, 2},
> >  {16, 15, 14, 13, 12, 11, 10, 9, 6, 5, 7, 8, 1, 2, 3, 4},
> >  {14, 16, 13, 5, 1, 12, 7, 4, 6, 11, 15, 10, 3, 2, 9, 8},
> >  {15, 4, 2, 5, 7, 3, 11, 6, 1, 10, 16, 13, 9, 8, 12, 14}}
> >
> >
> >
> > {{1, 14, 12, 11, 8, 6, 5, 4, 7, 9, 2, 3, 10, 13},
> >  {2, 1, 7, 9, 10, 11, 4, 3, 6, 5, 8, 12, 13, 14},
> >  {4, 2, 1, 10, 11, 8, 9, 5, 6, 7, 12, 13, 14, 3},
> >  {5, 3, 8, 7, 1, 2, 9, 6, 10, 11, 12, 13, 14, 4},
> >  {11, 9, 10, 3, 4, 5, 12, 13, 6, 7, 14, 2, 8, 1},
> >  {9, 5, 4, 7, 6, 8, 10, 11, 12, 13, 14, 1, 3, 2},
> >  {13, 9, 10, 11, 12, 14, 1, 6, 8, 5, 4, 2, 3, 7},
> >  {12, 9, 13, 14, 11, 5, 1, 6, 10, 2, 3, 4, 7, 8}}
> >
> >
> > Gruss
> > Udo.
> >
> > > welche Eigenschaften haben die folgenden Matrizen gemeinsam?
> > >
> > > {{1, 10, 9, 12, 11, 3, 6, 4, 8, 7, 5, 2},
> > >   {2, 1, 10, 11, 5, 12, 3, 7, 4, 8, 6, 9},
> > >   {4, 2, 12, 1, 9, 3, 8, 11, 10, 6, 7, 5},
> > >   {5, 4, 3, 2, 11, 1, 12, 9, 7, 8, 6, 10},
> > >   {7, 8, 1, 5, 9, 4, 2, 12, 10, 3, 11, 6},
> > >   {8, 9, 6, 12, 2, 3, 5, 4, 10, 11, 7, 1},
> > >   {10, 12, 5, 6, 9, 11, 4, 8, 2, 7, 1, 3}}
> > >
> > >
> > >
> > > {{1, 10, 3, 6, 7, 9, 8, 4, 5, 2},
> > >   {2, 1, 9, 7, 10, 8, 3, 5, 6, 4},
> > >   {4, 2, 1, 10, 5, 9, 3, 7, 8, 6},
> > >   {5, 3, 7, 6, 2, 1, 4, 10, 9, 8},
> > >   {9, 4, 3, 10, 6, 1, 2, 7, 8, 5},
> > >   {10, 8, 7, 5, 9, 4, 3, 6, 2, 1}}
> > >
> > >
> > >
> > > {{1, 8, 6, 4, 5, 7, 3, 2},
> > >   {2, 1, 8, 3, 7, 6, 5, 4},
> > >   {4, 2, 1, 3, 8, 7, 5, 6},
> > >   {5, 8, 3, 4, 2, 6, 1, 7},
> > >   {8, 4, 5, 6, 3, 7, 2, 1}}
> > >
> > >
> > >
> > > {{1, 6, 4, 3, 5, 2},
> > >   {2, 1, 6, 4, 5, 3},
> > >   {4, 2, 6, 3, 5, 1},
> > >   {5, 3, 2, 6, 1, 4}}
> > >
> > >
> > >
> > > {{1, 4, 3, 2},
> > >   {2, 1, 4, 3},
> > >   {4, 2, 3, 1}}
> > >
> > >
> > >
> > > {{1, 2},
> > >   {2, 1}}
> > >
> > >
> > >
> > > {{1}}
> > >
> > >
> > >
> > > Mit den besten Grüssen
> > > Udo.