For any 10 digit natural number [tex]N[/tex] in which(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Very clever and difficult number theory puzzle (with generalization)

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