Moin moin
im Quantamagazine steht eine Aufgabe von J. H. Conway
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https://www.quantamagazine.org/three-math-puzzles-inspired-by-john-horton-conway-20201015/
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There is a mysterious 10 - digit decimal number, abcdefghij.
Each of the digits is different, and they have the following properties :
* a is divisible by 1
* ab is divisible by 2
* abc is divisible by 3
* abcd is divisible by 4
* abcde is divisible by 5
* abcdef is divisible by 6
* abcdefg is divisible by 7
* abcdefgh is divisible by 8
* abcdefghi is divisible by 9
* abcdefghij is divisible by 10
What' s the number?
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Ein Kandidat kann mit
Clear[conwayQ]
conwayQ[o_Integer?Positive] := Block[{l = IntegerDigits[o]},
(DeleteDuplicates[l] == l) && Union[Mod[FromDigits[Take[l, #]], #] &
/@ Range[10]] == {0}
] /; Length[IntegerDigits[o]] == 10
geprüft werden, z.B. dieses x:
In[200]:= IntegerQ[x] && Positive[x]
Out[200]= True
In[201]:= conwayQ[x]
Out[201]= True
das iss'es doch.
Grüsse
Udo.
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