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?

Tom's house number is 81

I think I may have difficulty explaining how I got this, but I'll give it a shot.

The key is the last question: "Is the first digit 3?". John would only ask this if the number set he had left was small enough to narrow this down to one number. The only set of answers Tom could've have given him is (in order) No, Yes, Yes, and then either Yes or No for the last. Any other combination of answers would've left too many numbers for John to narrow down.

Since Tom answered truthfully to the 3rd question, we know it's a square.

Tom lied to the first question, so it is above 50.

This leaves 64, 81, and 100.

And it's not a multiple of 4.
Thus the number is 81.

So, am I even close?

Posted by Happy on 2002-05-30 12:02:28