Monday, 12 November 2012

8 ball select lighter ball from them

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Just Example : "Given 8 cue balls , one is weighing lesser than other 7. Find that(light weight) ball using just 2 chances on balance weight."
How to find a general solution to these kind of question? How to divide this set of balls? Is there any finer method or general formula?

Divide in group such that each group contain elements equal to certain power of 3 which is nearest to the total number of elements ..
for example if total 25 elements are given divide in groups of 9 element each so there will be 2 groups of 9 elements and 1 group of 3 elements .. each group will be further divide into 3 groups of 3 element each ....
coming to given problem of 8 cue balls .. divide into 3 groups ..
2 groups of 3 elements each .. say A and B
1 group of 2 element ..
put group A and B in balance ... there are 3 cases ..
case 1) if side with group A is lighter then remove the groups from balance and choose any 2 balls from group and put on balance .. if any one of them is lighter then u will directly know but if the balance is balanced then its the third ball (the one which u didnt put on balance) ..
case 2) if side with B on it is lighter .. apply the same logic as above ..
case 3) if balance is balanced then its the group 3 .. take the given 2 balls and put it on balance ... u r done :)

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