Finding the Fake Coin in 3 Weightings

  • Thread starter didi
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In summary, the problem is to identify a fake coin out of 12 coins, using a pan scale and no more than 3 weightings. The fake coin's weight is unknown and the task is to determine if it is heavier or lighter than the rest of the coins. This problem is considered to be famous and has caused difficulties for individuals during WW2. The solution can be found online, but it is recommended to try solving it and sharing thoughts before looking for the answer. It is suggested to start with 3 coins in 2 weightings.
  • #1
didi
3
0
Hi,
I have the following to solve and I tried so many things but it is confusing. Here is the problem
Given 12 coins such that exactly one of them is fake (we don't know if it is heavier or lighter than the rest), and a pan scale, devise a procedure to identify the fake coin and whether it is heavier or lighter by doing no more than 3 weightings.

Thank you :smile:
didi
 
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  • #2
A very famous problem that is alleged to have caused many problems with people at some important mathematical institution during WW2 (bletchley?) as they spent too much time trying to solve it. I'm sure that if you really don't want to spend time proving it the answer is googlable. But you really ought to try it and at least post your musings here. Though undoubtedly some one will sadly post the solution for you.
 
  • #3
Try solving it with 3 coins in 2 tries first
 

1. How many coins are needed for the 3 weightings?

The minimum number of coins needed for the 3 weightings is 12. This is because in each weighing, we can divide the coins into 3 groups of 4 coins each.

2. How many times can the scale be used in the 3 weightings?

The scale can be used a maximum of 3 times in the 3 weightings. In each weighing, we can compare 2 groups of coins, leaving 1 group untouched.

3. Can we determine whether the fake coin is heavier or lighter in the 3 weightings?

No, the 3 weightings method only allows us to determine which group of coins the fake coin is in, but not whether it is heavier or lighter. To determine this, we would need to use a different method with more weightings.

4. Is it possible to find the fake coin in less than 3 weightings?

Yes, it is possible to find the fake coin in less than 3 weightings. This would require using a different method or having fewer coins to weigh.

5. Can the 3 weightings method be used for any number of coins?

Yes, the 3 weightings method can be used for any number of coins. However, the minimum number of coins needed for this method to work is 12.

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