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American Coins Which One Should You Collect by madcore

Main purpose of this article is to give you an insight on the topic and guide you further into understanding everything related to this subject.

If you are interested in American history, as a Coin Collector there is a great deal of American coins to be found. There is a great amount of information about American coins. Finding this material is probably the best way to understand what types of American coins are good to have in your coin collection.

Above all the best resource to find good data about American coins is surely the internet. You will find a great quantity of pages about different American coins, you will find information about what sort of condition your American coins must be in to be considered as being valuable. In addition to that you can also find information about the kind of coins that were used in the civil war and pre-civil war times. These types of American coins are rare but they come on the coin market once in a while. Being informed about those types of coins will help you identify them if you come across them.

While this is true these American coins are not the only one that are considered as being good to have in your collection. Here is just a small sample of coins you could be concerned about:

- Dime piece (issued almost at the very beginning of the formation of the United-States)

- American coins with unusual face designs

- American Coins with small mistakes on them

- And many more

Sometimes, the errors you find on coins including American coins are what make them unequalled for Coin Collectors. Gather as much Information as possible about coin grading. This will help you greatly when you start seriously collecting coins. Since there is a great amount of American coins you can buy the information you have gathered will help you distinguish the characteristics that are the hallmark of valuable coins.

Small hint!

You may want to have coin folders for all of the American coins in your collection. This will help you see the various changes that have occurred to these different denominations. You can also categorize them by period of time. For instance as Kennedy coins are within reason hard to find you may want to see what other coins from that period of time have as unusual histories.

Soon you may discover that American coins are a testament to the history that as passed us by without our even knowing.

I hope that the information above was useful to you. Cheers and thank you for reading.

The coin-collecting-tips.com Website is the best place to learn more about various aspects of Coin Collecting . Get More info about American Coins . Read our guide for Beginners: How to become a coin collecting expert"

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Out of 80 coins, one is counterfeit. What is the minimum number of weighings need to find out the counterfeit?

Please explain your answer.

I assume that this is one of those problems where you are weighing the coins relative to each other on a balance scale.

One weighing would suffice, if you happened to pick the right two coins (and if you knew whether the counterfeit was heavier or lighter).

If you know whether the counterfeit coin is heavier or lighter, then there are 80 possible cases, corresponding each of the 80 coins. Each weighing has 3 possible outcomes (1. Left side heavier, 2. Right side heavier, 3. Sides balance), so 4 weighings can have 3^4 = 81 different outcomes, which suffices to distinguish all 80 cases.

If you don't know whether the counterfeit coin is heavier or lighter, then there are 160 possible outcomes, corresponding to each of the 80 coins being either heavier or lighter. Each weighing has 3 possible outcomes. Four weighings do not suffice, since they only distinguish 80 different cases. But five weighings distinguish 3^5=243 different cases, which is plenty to identify the bad coin & whether it is heavier or lighter than the rest.

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Edit: Mr. Causality has given an interesting argument, but I think his formula overestimates the number of weighings required. For instance, his formula says that 4 weighings are needed to find the counterfeit among 9 coins. My analysis says that 3 weighings are enough. Here is an algorithm showing that 3 weighings suffice:

Divide the 9 coins into 3 piles of 3, which we represent as sets:
Pile A: {1, 2, 3}
Pile B: {4, 5, 6}
Pile C: {7, 8, 9}
In the following we will indicate which is the heavier side with the "greater than" sign; for example {1,2,3} > {4,5,6} indicates that the pile of coins 1, 2, and 3 is heavier than the pile of coins 4, 5, and 6:

First weighing: {1,2,3} vs. {4,5,6}

If {1,2,3} > {4,5,6}

- Second weighing {1,4} vs. {2,5}

- If {1,4} > {2,5}

-- Third weighing {1} vs. {4}
-- If {1} > {4}, then 1 is the counterfeit and is heavier
-- If {1} = {4}, then 5 is the counterfeit and is lighter

- If {1,4} < {2,5}
-- Third weighing {2} vs. {5}
-- If {2} > {5}, then 2 is the counterfeit and is heavier
-- If {2} = {5}, then 4 is the counterfeit and is lighter

- If {1,4} = {2,5}
-- Third weighing {1} vs. {3}
-- If {1} < {3} then 3 is the counterfeit and is heavier
-- If {1} = {3} then 6 is the counterfeit and is lighter

If {1,2,3} < {4,5,6}, we follow a procedure symmetric to the one described above, which suffices to determine whether any of the coins 1-3 are counterfeit and lighter, or any of the coins 4-6 are counterfeit and heavier.

Finally, if {1,2,3} = {4,5,6}, then
- Second weighing {7} vs. {8}
- If {7} > {8}
-- Third weighing {7} vs. {9}
-- If {7} > {9} then 7 is the counterfeit and is heavier
-- If {7} = {9} then 8 is the counterfeit and is lighter

- If {7} < {8}
-- Third weighing {7} vs. {9}
-- If {7} < {9} then 7 is the counterfeit and is lighter
-- If {7} = {9} then 8 is the counterfeit and is heavier

If {7} = {8}
-- Third weighing {7} vs. {9}
-- 9 is the counterfeit and is heavier or lighter accordingly as it compares to 7.
____

Edit again: I see now the meaning of Mr. Causality's formula. It is elegant and correct. Give him the points.