Origin of the question is following.
You are faced a door to enter the magic land.
You should solve the problem given by the gate-keeper.
The gate-keeper chooses a positive integer. In order to solve the problem, you say a number per one trial to the gate-keeper.
If your number is equal or greater than the answer, the gate-keeper shouts “Sh!”.
If your number is less than the answer, the gate-keeper shouts “Brabo!”
You must provide the exact number to the gate-keeper.
You are allowed six times to say an answer.
Moreover, after the gate-keeper says “Sh!” three times, you have to say the exact answer.
Question 1 : What is the greatest number chosen by the gate-keeper in order that there always exists the way to solve the problem?
Question 2 : Then, by the Question 1, What is the number to say first in order to state to the exact answer?
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