You are given 8 coins. Of the 8 coins, 1 of them is a counterfeit coin which is lighter than the other coins. You are provided with a balance weighing scale. Using the balance weighing scale at most twice, explain the steps which you would take to identify the counterfeit coin.
Label the coins. ( 1 , 2 , 3 , 4 , 5 , 6 , 7 & 8 )
Group coins 1,2,3 together and 4,5,6 together . Leave the remainder coins aside ( 2 of them : 7 & 8 )
Step 1: Weigh coins 1,2,3 and 4,5,6 together as a set . Make sure you weigh them differently and record the readings . If they are weigh the same , the counterfeit coin is not in these groups and it has to be coin 7 or 8.
Step 2: Weigh coins 7 and 8 seperately, the lighter one is the Counterfeit coin.
IF
If coins 1,2,3 and 4,5,6 do not weigh the same, the lighter group contains the Counterfeit Coin.
For example if coin 1,2 or 3 is the Counterfeit, it will be lighter than coins 4,5 and 6.
So, to find out which is the Counterfeit, we will weigh coins 1 and 2 first.
If they are weigh equally, coin 3 is the Counterfeit.
But if they do not weigh the same, the lighter coin is obviously the Counterfeit.
VERSION 2
Now, you are given 9 coins and 1 of them is a counterfeit coin. The counterfeit coin is heavier than the good coins. Explain how you would find the counterfeit coin using the balance weighing scale in only 2 weighings.
Using the same method, we'll group coins 1,2 and 3 together, 4,5 and 6 together and 7,8 and 9 together as a group.
Step 1: Weigh coins 1,2,3 and 4,5,6. If they are weigh the same, the Counterfeit is either coin 7,8 or 9.
Step 2: Weigh coins 7 and 8, if they weigh the same, coin 9 is the Counterfeit. But if it weigh differently, the heavier coin is the Counterfeit.
If coins 1,2,3 and 4,5,6 are unbalanced, the heavier side contains the Counterfeit.
For example if coin 1,2 or 3 is the Counterfeit, it will be heavier than coins 4,5 and 6.
So, to find out which is the Counterfeit, we will weigh coins 1 and 2.If they are balanced equally, coin 3 is the Counterfeit.But if they are unbalanced, the heavier coin is the Counterfeit.
VERSION 3
Now, you are given 12 coins and 1 of them is a counterfeit coin. The counterfeit coin may be heavier or lighter than the good coin. Explain how you would find the counterfeit coin using the balance weighing scale in only 4 weighings.
Group coins 1,2,3,4 together, 5,6,7,8 together and 9,10,11,12 together as a same group.
Step 1: Weigh coins 1,2,3,4 and 5,6,7,8, if they are weigh the same, coins 9,10,11,12 contains the Counterfeit.
Step 2: Weigh coins 9,10 and 1,2 if they are equally balanced, the Counterfeit is either coin 11 or 12. But if it is unbalanced, weigh coin 9 and 1. If it is equally balanced, coin 10 is the Counterfeit, if it is unbalanced, coin 9 is the Counterfeit.
If coins 1,2,34 and 5,6,7,8 are not equally balanced..
Step 2: Weigh coins 1,2,3,4 and 9,10,11,12, if they are equally balanced, the Counterfeit is either 5,6,7 or 8. But if it is unbalanced, the Counterfeit is the 1,2,3 or 4 coins.
Step 3: Weigh coins 7,8 and 11,12 . If they are equally balanced, the Counterfeit is either 5 or 6 .
Step 4: So, to find out which is the Counterfeit, weigh 5 and 1, if it is unbalanced, it is the Counterfeit. But if it is equally balanced, 6 is the Counterfeit.
But if they are unbalanced, the Counterfeit is 7 0r 8.
Step 4: So, to find out which is the Counterfeit, weigh 7 and 1, if it is unbalanced, it is the Counterfeit. But if it is equally balanced, 8 is the Counterfeit.
This are the methods to solve the counterfeit problem . I hope you enjoyed it . Happy holidays ! (:
