Today, I was asked a very beautiful Logic Question by a very brilliant person. I took a minute to think about it and solve it. But then I was soo amazed at my own intelligence and aptitude that I am posting about the problem and my solution. (Sorry for bragging but I wonder how a brain works if not by divine intellect.)
Here is the question:
Question: You have got 90 pool balls which look completely identical in shape, size and weight. Only one ball in the complete set has a lighter mass. You also have a weighing machine. Tell me a way where you can find the anomalous ball in least number of iterations (steps).
Well, I have never come across such a puzzle till now, and was a bit dazed in such a scenario.
Then I trusted myself and started to think, and the solution was brilliant:
Doing it linearly weighing each ball takes 89 iterations.
My solution:
Divide the entire set of 90 balls into 45 each,
Weigh them on the weighing machine.
You get the set containing the ball with lighter weight.
Questioner: Okay, but wait, for the next iteration, how can you divide 45 balls into two sets?
Me: I am going to divide the whole set of 45 balls into two sets of 22 balls each plus one ball extra.
I weigh them. If both the new sets are of same weight, the extra ball would be the light ball,
If not, we get the set which contains the lighter ball, the set has 22 balls now.
Questioner: Okay, but it takes longer than the official answer.
Let us analyze then-
Official Answer
Divide the whole set into 30 ball sets of three.
Within 2 iterations, we get a set containing 30 balls,
Divide the set again into 10 ball sets, do the same.
To get lightest ball, the worst case scenario is 8 iterations.
My Answer
Within two iterations, you get a set containing 22 balls each.
Doing the same procedure, we get the Lighter Ball within 5 iterations.
Here is the question:
Question: You have got 90 pool balls which look completely identical in shape, size and weight. Only one ball in the complete set has a lighter mass. You also have a weighing machine. Tell me a way where you can find the anomalous ball in least number of iterations (steps).
Well, I have never come across such a puzzle till now, and was a bit dazed in such a scenario.
Then I trusted myself and started to think, and the solution was brilliant:
Doing it linearly weighing each ball takes 89 iterations.
My solution:
Divide the entire set of 90 balls into 45 each,
Weigh them on the weighing machine.
You get the set containing the ball with lighter weight.
Questioner: Okay, but wait, for the next iteration, how can you divide 45 balls into two sets?
Me: I am going to divide the whole set of 45 balls into two sets of 22 balls each plus one ball extra.
I weigh them. If both the new sets are of same weight, the extra ball would be the light ball,
If not, we get the set which contains the lighter ball, the set has 22 balls now.
Questioner: Okay, but it takes longer than the official answer.
Let us analyze then-
Official Answer
Divide the whole set into 30 ball sets of three.
Within 2 iterations, we get a set containing 30 balls,
Divide the set again into 10 ball sets, do the same.
To get lightest ball, the worst case scenario is 8 iterations.
My Answer
Within two iterations, you get a set containing 22 balls each.
Doing the same procedure, we get the Lighter Ball within 5 iterations.
All this without even referring to the internet.
All this was solved within minutes of the question and I was so thrilled that I am posting this onto my blog.
It is really amazing how the mind works!
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