Can somebody describe their solution to http://codeforces.me/gym/100519/problem/I ? Somehow I can't shake the feeling that it's enough to always multiply with 2, but I cannot substantiate my intuition to turn this into an algorithm.
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The first one is more along the lines of what I was thinking :) The second idea is magical.
It became one of my favourite problems few days ago :)! Indeed, we will use just multiplying by 2. Consider fraction
. If we have a fraction f, we multiply it by 2 and then receive information ">" we know that 
and if we receive "<", we know that 
. Inductively if we receive informations "<<>><><" and we change each "<" to "1" and ">" to "0" (unless p! = 2 we can't receive "=") we got a prefix of binary representation of f (following "0."), so "<<>><><" changes to "0011010" and we know that 
. Using 40 questions we can get approximation of 
with error at most 2 - 40, but if 
and 
are potential starting fractions we know that 
, so this precision is sufficient to uniquely determine starting fraction :)!
Oh wow, that's a really nice solution! Thanks for sharing.
Amazing！
Oh my god
A wise man.^_^