I am 1/3 Cherokee, as my dad was 1/3 Cherokee and my mom was 1/3 Cherokee, and (1/3 + 1/3)/2 = 1/3. In turn, my dad was precisely 1/3 Cherokee because his dad and his mom were both 1/3 Cherokee. And their parents as well, ad infinitum. My heritage is 100% 1/3 Cherokee.
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I am pretty confident that there is no power of 2 that is divisable by 3. I just spend 2 min throwing something together in python and for the first 200 I couldn't find one
So to get to 1/3 we need to find a base that is a power of 2 and can be devided by 3. And that doesn't seem to exist.