Alice moved to nolteight street. Bob meets her after her move, and he knows that the smallest house number in nolteight street is 8, and the highest number is 100. But he does not know Alice's house number.
Bob asks her: "Is your house number greater than 50?" Alice's answer is a lie.
Bob asks further: "Is your house number a multiple of 4?" Alice's answer is a lie again.
Bob continues: "Is your house number a square number?" Alice answers with the truth.
Finally Bob asks: "Is the first digit of your house number the number 3?".
Alice's answer is unknown.
Bob didn't notice that Alice lied on some of his questions, and answers with a house number. Alice says: "Your house number is wrong. However I gave you the wrong answer to your question asking if 3 is the first digit of your house number." Now Bob answers with a different house number.

What is Alice's house number?


2 Answers 2


I think her house number is


Reasoning is

For Bill to think he knows the answer after the four questions, he must have been given the answers 1) < 50 2) multiple of 4 3) square number

And then

he would pick either 16 or 36 depending on the answer to question 4, and his second answer would be the other one.


her real house number is >50, not a multiple of 4 and a perfect square. Thus 81 and not 64 or 100.

This also means

her original answer to 4) was that it began with 3, and his first guess was 36, second guess was 16


(SteveV was first to answer)

Alice's house number is


Bob's last answer tells us that

She answered that her house number is not > 50, which is a lie.

The only answers that allow Bob to submit a house number is

Number is not > 50 (a lie)
Number is multiple of 4 (a lie)
Number is a square number (the truth)
Which has only two solutions: 16 and 36, that's why Bob finally asked if the house number begins with a 3

Now that we know Alice's answers,

81 is the only number that satisfies greater than 50, not multiple of 4 and a square number


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