[chasing]

Yeah, but how many powers of 2 have all odd digits?

[Someone]

2^0 = 1

If we allow cheating, there are infinitely many. 2^(^2log(3.57)) equals 3.57, for example.

[317070]

2^0 and 2^{-1}. other positive integers will end on an even number, other negative integers will end with the numbers 25.

[detaro]

0

[ddalcino]

I think you forgot one.

[SamBam]

Nice double-meaning.

[joshuaissac]

> 0

2^0 is a power of two and has all odd digits.

Edit: If we include negative powers, there is also 2^-1, which is all odd except for the leading zero before the decimal point.