Numbers in mind puzzle
John has one of the numbers 1, 2, or 3 in mind. Jacob is allowed to ask one question to John to find out which of these three numbers he has in mind. John will answer this question only with the answers “yes”, “no”, or “I don’t know”.
Which question should Jacob ask John to find out in one time which number he has in mind?
I found a simpler answer than the one i gave above. Jacob will ask:
If you subtract 2 from your number, will the result be positive?
No means the chosen number is 1.
I don’t know the chosen number is 2 (since zero in neither positive nor negative)
Yes means the chosen number is 3.
Jacob will ask “Is the number in your mind greater than 2″?
If John says”Yes”, then it is obviously 3.
If he says”No”, then it is obviously 1.
If he says”I don’t know”, then it is 2 because, 2 is not greater than 2.
Similarly the question can be asked as ” Is the number in your mind less than 2″? and the same strategy be applied.
Jacob will ask: If I’ll draw a function of the degree of the number you have chosen will it have extremum?
A 1st degree function is a straight line so the answer is no.
A 2nd degree function has an extremum point so the answer is yes.
A 3rd degree function might have an extremum point but not always’ so the answer will be “I don’t know”
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