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Originally Posted by kmdivya
hi chetna n vineet thanks a lot for ur answers...pls help me sove this
There are 9 coins. Out of which one is odd one i.e. weight is less or more. How many iterations of weighing are required to find odd coin? the answer given is 3....but wat i get is 2
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Solution:
Lets divide the coins in group of 3 each ...
Now since we dont know whether the defective coin is heavier or lighter.So, we take the first 2 groups of three coins and weigh them on a pan balance ..keep each group on either side.
Now there may be two cases ...
Case1: if the balance shows inequality on both sides ..its for
sure that either of these groups has the defective coin.We also take into account that which pan of the balance goes up nd which goes down...(important ) .....(a)
now we take any one group out of this and weigh it with the left third group.
if the balance shows equality then the defective coin was in the other group which we weighed earlier.
or if there is inequality it means the defective coin is in the group common to both the weighing cases we have taken ..
So till now we have considered just 2 steps.
Now after knowing which group of 3 coins has the defective one ...
we will finally take any 2 coins out of the reamining 3 ..nd weigh them ...
if the weight is equal ...then the 3rd coin left is defective . if the weight is unequal .then we see that which side of the pan has gone up and which has gone down.........(b)
now considering the points (a) and (b)
we can easily know the defective coin nd whether it is heavier or lighter ...
This was the worst case scenario .and it took 3 steps to determine the defective coin as well as the fact that whether it was heavier or lighter .
Case2: If the result of weighing first two groups shows equality by the balance ..then the defective coin is in third group..
now since from the previous weighing we dont get an idea whether the coin is lighter or heavier ..
we have to perform two more steps in weighing the remaining three coins which wud perfectly determine the defective coin and whether it is heavier or lighter than the rest coins ...
in the left 3 coins we take any 2...
Case2.1)
if the weight is equal the defective coin is the third ...we can know here the defective coin in only two steps but we cud not determine whether it was heavy or light..
so one more step by weighing the defective coin with one of the equal coins wud determine if the defective coin is heavier or lighter ..although the question doesnt aske us to determine the lightness or heaviness of the coin to be found...
Case2.2)
If by weighing any two coins in the left lot we get inequality. we again weigh one of these two coins with the third one keepin g in mind which side of the pan balance went up and which side went down in the previous weighing.
then in these two steps plus the previous step we wud know that which is the defective coin and is it heavier or lighter..
hence in total 3 iterative steps required ..