John is tryng to locate Tom's house. All he knows is that Tom lives on a street with houses numbered from 8 to 100.
John asks Tom:
"Is your house number bigger than 50?"
Tom answers him, but he lies. (John doesn't know that he's lying) John continues to ask:
"Is your house number a multiple of 4?"
Tom answers and again, he lies. Then John asks:
"Is your house number the square of an integer?"
Tom answres, but this time he tells the truth.
Finally, John asks:
"Is the first digit of your house number 3?"
After Tom answers (we don't know if he lied or not) John declares Tom's house number, but he is wrong!
What is Tom's house number?
This one wasnt that hard, but still fun :)
By John asking if the number began with 3, we know that the answer to his first question(Is the number bigger than 50?) was no, when in fact it is greater than 50. Also the question that Tom answered rightly lets us know that the number would have to be a perfect square between 8 and 100 and since we know that it is greater than 50, that leaves 64, 81 and 100. Asking if it is divisible by 4 and then asking if it begins with a 3 lets us know that Tom told John it was divisible 4 and John was thinking 36. 64 and 100 are divisible by 4, so the answer is 81.
Eureka
