# Find the Detect Fake Coin with 3 Balance Scale Uses

In summary, there is a problem where you have 10 coins and a balance scale, with one fake coin that could be lighter or heavier. You are only allowed to use the scale 3 times and need to determine which coin is fake. The suggested solution is to divide the coins into two sets of 5 and weigh them, but this only tells you that one set is heavier than the other and does not help identify the fake coin.
You have 10 coins and a balance scale. 1 coin is a fake, but you don't know whether it is lighter or heavier than the rest. You are only allowed to use the scale 3 times. Which coin is fake?

I don't know the answer to this problem.

Can you use a graduated cylinder and water? ;-)

Try this:
90+ %
--- = balance scale;
1) 3 coinsA --- 3 coinsB than 2) 3 coinsA or B --- 3 coinsC than you know what group of 3 coins is lighter or heavier 3) spli the group ... 1 coin --- 1 coin and you solve it. But...if all 3 groups (A,B and C) are the same weight, the last coin is the one, but you don´t know if it´s lighter or heavier. :)

"Some times you don´t have to be exact, you have to be enough."

I´m sorry, that was 100%.

If one is lucky, it can be done in 2 trials. 5 v 5, 2 v 2, odd one out.

http://192.220.96.182/trap_a1.html#14

Separate the coins into 3 groups of 3 and a single (A, B, C, and S). Weigh A and B, then B and C (taking note of which is heavier or lighter in both weighings (if both weighings balance, then S is the counterfeit coin). Based on the two weighings you can tell which group of three had the counterfeit coin AND whether it was lighter or heavier than the others. You then weigh two of the three coins in the suspect group (one on each scale). If they balance, then the third coin of the group (not weighed) is the counterfeit. If they do not balance you will know which of the two is counterfeit because you were able to determine whether the counterfeit coin was heavier or lighter from the previous two weighings.

Last edited by a moderator:
GDBot said:
If one is lucky, it can be done in 2 trials. 5 v 5, 2 v 2, odd one out.

No, it can't. 5v5 will only tell you that one set is heavier than the other. Since you don't know what the fake coin is, the first weighting tells you nothing.

## What is the purpose of "Find the Detect Fake Coin with 3 Balance Scale Uses"?

The purpose of "Find the Detect Fake Coin with 3 Balance Scale Uses" is to determine which of a group of coins is fake by using a balance scale with 3 pans.

## How does the 3 balance scale method work?

The 3 balance scale method involves dividing the coins into 3 groups and weighing 2 groups against each other. If the weights are equal, the fake coin is in the third group. If one group is lighter, the fake coin is in that group. If one group is heavier, the fake coin is in the other group. This process is repeated until the fake coin is found.

## What is the minimum number of weighings needed to find the fake coin using the 3 balance scale method?

The minimum number of weighings needed is 2, as the first weighing will determine which group the fake coin is in and the second weighing will determine the fake coin within that group.

## Can the 3 balance scale method be used for any number of coins?

Yes, the 3 balance scale method can be used for any number of coins. However, it is most efficient when the number of coins is a power of 3 (3, 9, 27, etc.) as it allows for the most balanced groupings.

## Are there any limitations to the 3 balance scale method?

Yes, the 3 balance scale method may not work if the fake coin is not significantly lighter or heavier than the real coins. It also may not work if the fake coin is not present in the initial group of coins.

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