Question

Impossible ❤️

You have 12 coins; one weighs slightly less or slightly more than the others. Using an equal-arm balance and only making three weighings, determine which one is different, and whether it is slightly lighter or heavier. The fact that you don't know whether it is lighter or heavier up front makes this problem much more difficult than other similar problems. ​

Answer 1

Ultra impossible almost :-

There are 12 coins .

We have to make 3 weighings as specified .

We are told that one coin weighs slightly more than the others .

Let us name the coins :-

1 , 2 , 3 ...... 12

Let us divide the coins into groups :-

1 , 2 , 3 , 4 - first group .

5 , 6 .... 8 - second

9 , ..... 12 - third

We will weigh the first group and the second .

If the weights are equal , then the other group ( 3 rd ) has the unequal coin .

If the weights are unequal then do the following :-

If 5,6,7,8 has more weight :-

Measure the 1,5,6 with 2,7,8 .

If it balances equally , then :-

3 or 4 either one of them has the unequal coin . Measure their weights to find the correct coin which is fair as we are taking the measure 3 times .

If it does not balance then :-

Then we will see which one is heavier .

If the values of 1,5,6 is heavier :-

check among 5 and 6 then .

If 2,7,8 is heavier :-

check among 7 and 8 then .

Do the opposite for the other pile ( other possibility ) .

In case of the 3 rd having unequal :-

Check with 9,10 and 11,12 :-

If one is unequal then check that one again .

For eg : if 9,10 are unequal , check among 9 and 10 .

Hence by these methods we can check both whether the coin is light / heavy .

Answer 2

1. Divide into 4 groups of 3 each.

2. Weigh 1: Weigh any 2 groups

3. If step 2 balances, the light or heavier coin is in one of the other two geoups

If it doesn't balance, the different coin is within one of these two groups

4. Weight 2: Weigh any one grp of step 3 with third group of coins from step 1.

5. If step 4 balances, the group you just moved out from scale has the different coin.

If it doesn't balance, the group you just put on the scale in step 4 has different coin.

In step 5, depending upon the scale, you would also get to know if the coin is heavier or lighter from others.

6. Now you know which 3 balls has one different coins.

Weigh 3: Take any two coins of this group and weigh on scale.

If it balances, the third coin is heavier or lighter.

If it doesn't balance, you know in step 5 if it's heavier or lighter. Choose the side of scale accordingly and pick the heavy/light coin.