Downtime Puzzle, again

[GM-Ayu]

Seems like no one got this one so far, so the hint for question 4!


Hint: If I don't lie at all, then you only need 11 questions to do find the answer, so the 4 extra questions allowed are treated as "error detecting" questions. Consider the case where you have 11 coins. They are either heads, or tails. If lying isn't allowed, then you only need 11 questions to ask about them individually "is coin 1 heads? is coin 2 heads?" and so on. With this hint in mind about 11 questions for coins if there's no lying, think about how to relate this back to 1 to 2000.


(server is up again yes, but let's finish this one anyway.)