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Power Of $2$

Posted: Tue Feb 20, 2018 4:39 pm
by samiul_samin
Does there exist a natural number $N$ which is a power of $2$ ,such that one can permutate its decimal digits to obtain a different power of $2$ ?

Re: Power Of $2$

Posted: Tue Feb 20, 2018 4:43 pm
by samiul_samin
Think about the size of $2^k$ and $2^{k+4}$ for,$k=1,2,3,...$
Problem source
17th Iranian Math Olympiad
Solution source
You can get an elegant,awesome and titanic solution of this problem in this book:
(You can get the PDF easily by using internet.)