27 coins and the Grocer
A Grocer receives 27 coins from a customer as a payment for the vegetables. At the same time a famous magician visits him to buy his grocery and tells him that one of the coins is fake and is slightly heavier than the others .
The Grocer decides to check the coins , however another customer is in a hurry and says that he will leave if it takes too much time. The Grocer has only a pan balance ( two sided weighing scale which compares the weights and shows the heavier one).
how many times does he have to weigh the coins at minimum?
*If one coin is disturbed, touched,removed,moved,added to the pan balance etc it counts as one weighing. *Assume that the magician is telling the truth i.e. one coin is slightly heavier and fake *Assume that the rest of the coins weigh exactly same.
The answer is 3.
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divide the 27 coins in three groups of 9 and weigh any two. The odd one(if the 2 groups weigh equal, then the 3rd is odd, else the one which is heavier is odd) do this again to reduce the group of 9 coins to 3 and then again 3--> 1 odd coin