ask johnny answer

guess_number.txt

https://www.theguardian.com/science/2021/feb/08/can-you-solve-it-think-of-a-number

The suggested answer using "yes" and "no" amounts to encoding in base 2, which is inefficient because there are
three possible response options ("yes", "no", "I don't know"). We want to find a way of encoding in base 3, which 
amounts to assigning 1/3 of the numbers to "yes", 1/3 to "no", and 1/3 to "I don't know". We can do that by telling
Johnny on the first step (and analogously afterward):

"I have two numbers in mind. One of them is 334. The other is less than 667 but greater than 333, but I will not tell you what it is. Is your
number less than both of my numbers?" 

If his number is less than 334, he must answer "yes", because his number must be less than both of my numbers.
If his number is greater than 666, he must answer "no", because he knows that his number must be 
  greater than both of my numbers.
If his number is between 334 and 666 (inclusive), then he does not know whether his number is less than both, so 
  he must answer "I don't know".

Continuing in this way you can narrow down the possibilities to 1/3 of what they were at each step instead of 1/2, 
reducing the number of questions you need.