# math???????

you have 12 coins and one of them is counterfeit. you can weigh the coins 3 times only. after weighing 3 or less times how would you know which is counterfeit.

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First: 6 coins on one side, 6 coins on the other.

Result: Whatever side is heaviest has the fake coin.

Second: 3 coins on one side, 3 coins on the other, from the pile that was heaviest in step one.

Result: Again, the side that is heaviest has the fake one.

Third: Take any two coins of the three you have left and weigh them.

Result: If they are exactly the same weight then the one you have NOT wieghed is the fake. If one side is heavier than the other then that one is the fake.

Edit:

You can also do it this way:

Divide the coins into 3 piles of 4 coins each. Weigh one pile against the other. If they weigh the same the counterfeit coin is in the other pile of 4 coins. If they are of different weight, the counterfeit coin is in the heavier of the two pile. So, after one weighing you know that the counterfeit coin is one of 4 coins. Divide these 4 coins into 2 piles of 2 coins each and weigh them against each other. The counterfeit coin is one of the the two coins on the heavier side. Weigh these two coins against each other. the counterfeit coin is the heavier coin.

OOH, I came back to say that I thought about it and that we don’t know if the counterfiet is heavier or lighter and to adjust my answer, but found Bart’s answer which I totally agree with.

I vote Bart’s best answer! ;o)

.

this is answer assumes you know the weight of a real coin and the weight of the counterfeit.

1) weigh 6 of the coins, if the weight does not equal 6 x weight of real coin, then you know one of those 6 is counterfeit.(also if the 6 you weighed do equal the weight of 6 real coins, then you know the counterfeit is in the other stack of 6)

2) weigh 3 of those 6 coins, if the weight does not equal 3 x weight of real coin, then you know one of those 3 is counterfeit.

3) weigh 2 of those 3 coins, if the weight does not equal 2x weight of real coin, then one of them is counterfeit.

4) punch the person keeping track of how many times you are weighing the coins, and weigh one of the last 2 coins

Unlike other answers, we do not assume you know the weight of a real coin, nor do we assume that the counterfiet is necessarily heavier. We only make the (necessary) assumption that the counterfiet has a different weight, possibly heavier, but possibly lighter.

Number the coins 1 through 12

Step 1: weigh 1,2,3,4 vs. 5,6,7,8

Case 1: They Balance. Counterfiet is 9,10,11, or 12

Step 2: Weigh 9, 10, 11 vs. 1,2,3

Case 1.1: They balance. 12 is counterfeit

Case 1.2: The 9,10,11 side is light.

Step 3: Weigh 9 vs. 10 ; If they balance, 11 is bad. Else the one that is light is bad.

Case 1.3 The 9,10,11 side is heavy (Similar to case 1.2)

Case 2: 1,2,3,4 are light vs 5,6,7,8

Step 2: Weigh 1,2,5 vs. 3,4,6

Case 2.1 They balance. Either 7 or eight is bad.

Step 3: Weight 7 vs. 8. Heavy coin is bad.

Case 2.2 1,2,5 side is heavy. 3 or 4 light, or 5 heavy.

Step 3: Weigh 3 vs. 4. Light coin bad, balance if 5 is bad.

Case 2.3 1,2,5 is light; 1 or 2 light or 6 heavy. Similar to case 2.2