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?

Nice problem, Half-Mad. I solved this using a tree diagram, of the kind used in probability problems. Each branch is a binary "yes/no", followed by the possible numbers that answer generates. The solution pops out visually in a nice way with this method. If you're working on this problem and are stumped, try a tree diagram.

Posted by Rebecca Jaffe on 2005-09-16 07:18:06