Question

There are 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins. How to find the false coin by three weighs on a simple scale?

Answer 1

Given : 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins

To find : False coin by minimum weigh

Solution:

Lets make 3 Heap  of    4 Coins  Each  

and weigh 2 heaps with each other

if both are Equal  then    

Heavier or  Lighter  is  in 3rd Heap

if they are Heavier & lighter  then Check

one heap with 3rd heap to find  false coin is heavy or Light ( 2nd weigh)

then Take heavy or light coin ( what ever the case is )

take 1 coins in each Scale  

if heavier lighter then found  (in 3rd Weigh)

if Equal then check remaining two coins , one in each scale  (4th weigh)

Hence total 4 Weigh

another case

taking 3rd Heap

taking 1 Coins in each Scale   ( 2nd weigh)

if Heavier or lighter check with one coin of other heap to find lighter or heavier ( 3rd weigh)

if

Equal weight then  Check one coin from remaining Coins  (3rs Weigh)

and found false

There is one case where 4 weighing are required

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