Only that this is far from being new or original… this idea already appears in a much more sophisticated form in the phantastic book “Dzienniki gwiazdowe” from 1957 (!), published in english as “The Star Diaries” (1976) and “Memoirs of a Space Traveller” (1982) by the great (and sadly late) Stanislav Lem.
(see e.g. http://en.wikipedia.org/wiki/Stanisław_Lem)
well, it’s a pity that tigers are not more into math…hobbes could have told calvin to play the game with saying “no, higher” or “no, lower”.
by halving each interval, he could have guessed (even for this outrageously big interval) in log2(700,000,000,000) =~ 39.35 that is around 40 guesses.
not that bad, ain’t it? ;o)