- #1
mathwizarddud
- 25
- 0
For any 10 digit natural number [tex]N[/tex] in which
the first digit corresponds to the total no of 1's.
the 2nd digit corresponds to the total no of 2's.
.
.
.
the 10th digit corresponds to the total no of 0's.
determine, with proof, if the number of such natural number [tex]N[/tex] is finite, and if proved true, find them all.
A generalization of
http://answers.yahoo.com/question/i...lB5DIp8Cxgt.;_ylv=3?qid=20080628051813AA0p296
Also, extend this to any numerical base [tex]M[/tex] such that the [tex]M^{th}[/tex] digit corresponds to the total number of 0's and [tex](M - 1)^{th}[/tex] digit corresponds to the total number of [tex](M - 1)[/tex]'s for any natural number [tex]M[/tex], etc.
the first digit corresponds to the total no of 1's.
the 2nd digit corresponds to the total no of 2's.
.
.
.
the 10th digit corresponds to the total no of 0's.
determine, with proof, if the number of such natural number [tex]N[/tex] is finite, and if proved true, find them all.
A generalization of
http://answers.yahoo.com/question/i...lB5DIp8Cxgt.;_ylv=3?qid=20080628051813AA0p296
Also, extend this to any numerical base [tex]M[/tex] such that the [tex]M^{th}[/tex] digit corresponds to the total number of 0's and [tex](M - 1)^{th}[/tex] digit corresponds to the total number of [tex](M - 1)[/tex]'s for any natural number [tex]M[/tex], etc.