Question

Try this one:

If \( X = 2^n \), how many \( n \), positive integer, exist such that \( X \) does not
have a digit which is a power of \( 2 \)?

Answer 1

The difficulty of the problem lies in the proving or disproving the number of numbers of such form existence or non-existence.

Answer 2

\[1,2,4,8,16,32,64,128,256,512,1024,2048, \ldots\]
Might help lol

Answer 3

lol, Yes, but brute forcing won't give you any conclusive result though.

Answer 4

Is the Binomial Theorem any help here?

Answer 5

\[2^n = \sum_{k=0}^{n} \left(\begin{array}r n\\k \end{array}\right)\]

Answer 6

\(2\) I think.