Friday, December 30, 2011

Puzzle #1: 8 Billiard Balls

Question:

Suppose you had 8 billiard balls, and one of them was slightly heavier, but the only way to tell was by putting it on a scale against another. What's the fewest number of times you'd have to use the scale to find the heavier ball?

Answer:

First Split the 8 balls in a group of 6 and 2.

1st weigh - From the group of 6 balls weigh any 3 against the other 3.

2nd weigh - In 1st weigh if they are equal then we can infer that the ball that's slightly heavier is in the group of two balls, then we can weigh them against each other and find out the heavier one.

Else if one of the set of balls in the first weigh is higher than other we can infer that the heavier ball is in one of that 3 balls which is weighing heavier than the other 3. Then we can take two balls of those 3 and weigh against each other and find the heavier one, if both turn out to be of same wight then the third one is the heavier of all the eight balls.

So it takes totally 2 weighs to find the ball which is slightly heavier.
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