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# You have 12 balls. All of them are identical except one,

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Director
Joined: 26 Feb 2006
Posts: 899
You have 12 balls. All of them are identical except one, [#permalink]

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03 Jan 2007, 01:07
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You have 12 balls. All of them are identical except one, which is either heavier or lighter than the rest. The odd ball is either hollow while the rest are solid, or solid while the rest are hollow. You have a scale, and are permitted three weighings. Can you identify the odd ball, and determine whether it is hollow or solid?
Senior Manager
Joined: 24 Nov 2006
Posts: 349

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03 Jan 2007, 13:51
Could you pls determine whether the scale allows you to put two groups of balls and weight each against the other, or it is a plain scale?
Director
Joined: 26 Feb 2006
Posts: 899

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04 Jan 2007, 12:02
Andr359 wrote:
Could you pls determine whether the scale allows you to put two groups of balls and weight each against the other, or it is a plain scale?

it is allowed to scale in groups of 2 or 3 or 4 or so on..
Senior Manager
Joined: 20 Feb 2006
Posts: 373

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04 Jan 2007, 17:50
Would you not just weight 3 groups of 4 balls. The two groups of 4 that are the same weight will allow you to determine the weight of each ball. The 3rd set of 4 balls which contains the "odd one out" will either be lighter or heavier and so you'll be able to determine whether it's hollow or not.
Manager
Joined: 20 Dec 2004
Posts: 177

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04 Jan 2007, 22:20
According to me the probability is 1/8

First we need to find the probability of finding an odd ball in 3 weighings.

P(atleast 1 weighing is an odd ball)=1 - P(none of the weighings are odd)
=1 - (11/12)*(10/11)*(9/10)
=1 - 9/12
=1 - 3/4
=1/4

The probability of odd ball being solid or hollow is 1/2

Therefore the Probability of finding an odd ball and determining whether it is hollow or solid is 1/4 * 1/2=1/8
_________________

Regards

Subhen

04 Jan 2007, 22:20
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