# Out of 27 similar looking coins, one is fake coin whose weight is less than that of a genuine coin. If a beam balance is given to you (without any weight) check out of a strategy to detect the fake coin by using balance exactly thrice.

Dear Student,

Divide the coins into 3 groups with 9 coins each.

Step 1 : Start weighing with 9 coins on each side.

Scenario 1.1 : The balance shows a lighter side.  we choose that group of 9 coins .

Step 2 : Now again we divide the coins into 3 groups with 3 coins each. Start weighing with 3 coins on each side.

Scenario 2.1 : The balance shows a lighter side.  we choose that group of 3 coins .

Step 3 - Weigh any 2 coins of the coins .

Scenario 3.1 - One of them will be lighter .

Scenario 3.2 - If they are equal, the third unused coin is the lighter .

And

Scenario 1.2 - The balance shows equally weighed coins ( When we weigh with 9  coins in each side ) .

Step 1.2 - Pick the unused set.  then go to step 2 and follows .

So, we can say that we can find lighter  coin in three steps .                                              ( Ans )