Re: Kopfnuss[2]

[Wolfgang Ludwig <w.ludwig@XXXXXXX.de>]

Danke für den symmetrischer Jahresanfang:

In Worten:
Man drehe das Pascalsche Dreieck  um 120°  und 240° und summiere die 3
Zustände.

oder

Summe[Tabelle[RotationUmFlächennormale[Pascalsches Dreieck, Phi],{Phi,0,4
Pi/3,2 Pi/3}]


Implementierung z.B.

raetsel[ n_] :=
Module[{pasc1, pasc2, pasc3, m, k},
pasc1 = PadRight[#, n + 1] &/@ Table[Binomial[m, k], {m, 0, n}, {k, 0, m}];
pasc2 =Reverse@Transpose[pasc1];
pasc3 = Reverse /@ pasc2;
Plus @@Map[Cases[#, _?(# > 0 &)] &, {pasc1, pasc2, pasc3}, {2}]
]

Herzliche Grüsse

Wolfgang



Udo und Susanne Krause schrieb:

> Guten Abend zusammen,
>
> (1) wie kann man die Funktion Raetsel[n] /; NonNegative[n]
> implementieren und
> (2) kann man allenfalls die Implementation kurz und bündig in Worte
> fassen?
>
> Einige Werte sind:
>
> In[84]:=Raetsel[0] // TableForm
> Out[84]=
> {{3}}
>
> In[85]:=Raetsel[1]
> Out[85]=
> {{3},
> {3, 3}}
>
> In[86]:=Raetsel[2]
> Out[86]=
> {{3},
> {4, 4},
> {3, 4, 3}}
>
> In[87]:=Raetsel[3]
> Out[87]=
> {{3},
> {5, 5},
> {5, 6, 5},
> {3, 5, 5, 3}}
>
> In[88]:=Raetsel[4]
> Out[88]=
> {{3},
> {6, 6},
> {8, 8, 8},
> {6, 8, 8, 6},
> {3, 6, 8, 6, 3}}
>
> In[89]:=Raetsel[5]
> Out[89]=
> {{3},
> {7, 7},
> {12, 10, 12},
> {12, 12, 12, 12},
> {7, 10, 12, 10, 7},
> {3, 7, 12, 12, 7, 3}}
>
> In[90]:=Raetsel[6]
> Out[90]=
> {{3},
> {8, 8},
> {17, 12, 17},
> {22, 17, 17, 22},
> {17, 17, 18, 17, 17},
> {8, 12, 17, 17, 12, 8},
> {3, 8, 17, 22, 17, 8, 3}}
>
> In[91]:=Raetsel[7]
> Out[91]=
> {{3},
> {9, 9},
> {23, 14, 23},
> {37, 23, 23, 37},
> {37, 28, 26, 28, 37},
> {23, 23, 26, 26, 23, 23},
> {9, 14, 23, 28, 23, 14, 9},
> {3, 9, 23, 37, 37, 23, 9, 3}}]]\)
>
> In[93]:=Raetsel[8]
> Out[93]=
> {{3},
> {10, 10},
> {30, 16, 30},
> {58, 30, 30, 58},
> {72, 44, 36, 44, 72},
> {58, 44, 40, 40, 44, 58},
> {30, 30, 36, 40, 36, 30, 30},
> {10, 16, 30, 44, 44, 30, 16, 10},
> {3, 10, 30, 58, 72, 58, 30, 10, 3}}
>
> und zur Kontrolle etwa noch
> In[95]:=Raetsel[17]
> Out[95]=
> {{3},
> {19, 19},
> {138, 34, 138},
> {682, 138, 138, 682},
> {2382, 578, 216, 578,  2382},
> {6190, 1838, 556, 556, 1838, 6190},
> {12378, 4386, 1458, 748, 1458,  4386, 12378},
> {19450, 8026, 3090, 1322, 1322, 3090, 8026, 19450},
> {24312, 11458, 5088, 2278, 1500, 2278, 5088, 11458, 24312},
> {24312, 12888, 6516, 3252, 1908, 1908, 3252, 6516, 12888, 24312},
> {19450, 11458, 6516, 3672, 2256, 1836, 2256, 3672, 6516, 11458, 19450},
> {12378, 8026, 5088, 3252, 2256, 1848, 1848, 2256, 3252, 5088, 8026,
> 12378},
> {6190, 4386, 3090, 2278, 1908, 1836, 1848, 1836, 1908, 2278, 3090, 4386,
> 6190},
> {2382, 1838, 1458, 1322, 1500, 1908, 2256, 2256, 1908, 1500, 1322, 1458,
> 1838, 2382},
> {682, 578, 556, 748, 1322, 2278, 3252, 3672, 3252, 2278, 1322, 748, 556,
> 578, 682},
> {138, 138, 216, 556, 1458, 3090, 5088, 6516, 6516, 5088, 3090, 1458,
> 556, 216, 138, 138},
> {19, 34, 138, 578, 1838, 4386, 8026, 11458, 12888, 11458, 8026, 4386,
> 1838, 578, 138, 34, 19},
> {3, 19, 138, 682, 2382, 6190, 12378, 19450, 24312, 24312, 19450, 12378,
> 6190, 2382, 682, 138, 19, 3}}
>
> ... es symmetrische Anordnungen, wie man sieht ...
>
> Mit den besten Grüssen
> Udo.