In 80 coins 1 coin is counterfeit what is minimum number of weightings to find out counterfeit coin?
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Assuming you know if the coin is heavier or lighter, the answer is 4 weighings. Let’s assume the counterfeit coin is *lighter*.
Start by dividing the pile into 3 groups (27,27,27).
Weigh two of the groups. If one side goes up, it contains the light, counterfeit coin. If they balance, it is in the unweighed group.
Now repeat the process with the group of 27 you have found. This time divide it into 9,9,9.
Once you have figured out the group of 9, divide it into 3,3,3 and repeat the process.
Finally divide it into 1,1,1. The final (4th) weighing will discover the counterfeit coin.
Answer:
Assuming a balance scale and a known discrepancy (e.g. lighter), the answer is a minimum of 4 weighings, to guarantee finding the counterfeit coin.
Assume you do not know if the counterfit is light or heavy it will take 5 uses of a balance. The trick things into three groups. If it balances, the group you did not consider contains the flaw. If it does not balance the flaw is on the balance with groups called suspected light and suspected heavy.
Consider a simpler example
you can do 12 balls in 3 weighings
Let G be good H be suspected heavy and L be suspected
for the first trial you balance 4 and 4
if they do not balance it leaves you with
LLLL and HHHH
you use the good ones to learn something
trial 2 is
GGLL and LLHH
If it does not balance in the worst case you have 2 lights and 2 heavys to seperate
LH HG
I hope you get the idea
3 (unless you know what a non-counterfeit coin weighs)
1 counterfeit and 2 non-counterfeit