Expert: Surajit Basu - 4/15/2008

Question
you have a scale of justice and eight balls. seven balls weigh the same and one is heavier. you can not tell the heavier ball by holding it. if you can only use the scale twice. how do you determine the heavier ball?

Answer
take any three on one side; three others on the other side.

There are two possibilities: A and B.

A) If both are equal, then the remaining two contain the heavier ball.

Just weigh these two, the heavier one is it.


B) If one side is heavier, then that set of three contains the heavier ball.

Just weigh two of these three; if one side is heaver, the heavier one is it. If both are equal, the remaining one is it.

now, two questions:

what if you have 9 balls? can you do it in 2 weighings?
what if you have 12 balls? can you do it in 3 weighings?


Enjoy!