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?

We don't know how Tom answered the questions, but we do know that if a given sequence of answers will produce a unique solution before John asks the last question, or if it does not produce a unique solution even after John's last question, it cannot be the right sequence.

After we determine how Tom answered, knowing when he was lying and when he was telling the truth will allow us to find the correct answer.

Posted by TomM on 2002-05-30 12:00:38