Can you handle this riddle?
Jack lives in a long street. The number on his house is somewhere between 13 and 1300. Fred wants to guess Jacks number, so he asks:
"Is the number higher than 500?" Jack answers, but he lies.
Then he asks: "Is your number a square?" Jack answers again, and he lies again.
The next question is: "Is your number a third power?" Jack answers, and this time he speaks the truth.
Then Fred asks: "If I would know at this point whether or not the second digit in your number is a 1, I would know your number, right?" Jack answers.
Then Fred takes a guess, but guesses wrong. On what number does Jack live?
Hint: Fred and Jack are friends, so Fred assumes Jack is telling the truth to him always.
The answer is 64.
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1 solution
Fred must think there are only two possibilities left after hearing the first three answers; one with a '1' as second digit, and one with something else as second digit. There are eight possibilities of how the first three answers can be answered, as they are all yes/no questions. ( 2 3 =8). Only when the first three answers are respectively 'yes', 'no' and 'yes', there are two options left; 512 and 1000. And indeed, if these two options are left, Fred would know the answer if he would know whether or not the second digit was a '1'.
But Jack lied two times. The correct answers to the first three questions should be respectively: 'no', 'yes' and 'yes'. So we're looking for a number which is both a square and a third power, but is lower than 500. That has to be a sixth power. Because the number is also bigger than 13, the only option left is 2 6 , which is 64.
Therefore, Jack lives on number 64.