There are six billards balls, all of the same weight EXCEPT for one (1). You have three scales to work with to find out whether the ball of different weight is heavier or lighter than the rest. The catch is once you use a scale it immediately breaks and is unusable. Therefore you have to make a strategy in which you can determine if the ball is heavier or lighter in three tries.
According to the man who asked me this riddle, if you can solve it in under 47 minutes you are a math genius.
Good luck!
matbluvenger
9 Comments
There are 2 possible results: The scales are In or Out of balance.
IN BALANCE
You got lucky... the odd ball is one of the two you set aside.
Replace a pair on one side of the scale with the pair you set aside.
Note whether the new pair are lighter or heavier than the "normal" pair.
Weigh the 2 new balls against each other.
If the pair was lighter than the "normal" pair, the light ball is the odd one out.
If the pair was heavier than the "normal" pair, the heavier ball is the odd one out.
OUT OF BALANCE
This is the tougher option.
Note which side is heavier.
Swap 1 of the balls from the heavier side for 1 of the 2 "normal" balls you set aside.
There are two possible options: Change or No Change
CHANGE
Lucky! the removed ball is the odd ball and is heavy.
NO CHANGE
We know the ball you just swapped in is "normal" so the odd ball is one of the remaining original 3 still on the scales.
Weigh the 2 balls from the lighter side against each other.
Again, there are 2 possible results: The scales are In or Out of balance.
IN BALANCE
The removed ball is the odd ball and is heavy.
OUT OF BALANCE
The lighter of the two is the odd ball.
The key is the ball swap to determine whether the odd ball is light or heavy. It didn't take me very long... the majority of my time was spent in working out the wording and actually typing it in.
1) Post riddle to Woyano.
2) Wait until someone comes up with a solution.
3) Tell your friend that you are indeed a genius, because you smartly leveraged 21st century technology and the power of community to find what you wanted to know.
I once went to an interview that had riddles like these. When we got to the last one, which was impossibly difficult for me, and I was asked what I'd do, I said I'd hit up a search engine to see if someone else already had an answer, or failing that, see whether I could find enough information to develop an effective strategy for working out the solution. It's good to know our weaknesses and leverage available tools to overcome them in a timely manner, because then we can spend more time applying our strengths where they're needed.
I didn't get the job. :D
Hey you know AdGuy always gets the last word! ;)