How Can We Identify Counterfeit Coins?
Investigate the core facts How Can We Identify Counterfeit Coins supported by expert analysis.
We will give the Real coins a weight value of 1 and the fake a weight value of 2. Take any six coins of the eight coins, put 3 on the left side and three on the right side. If both sides equal 3, remove all six and weigh the remaining two. One of the two will be the fake coin and the second weighing will reveal it.
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Can you put a fake coin on a balance scale?
Solution. One weighing. Place one coin on one side of the balance scale, one on the other, and put one coin aside. If the scale balances, the coin that we put aside is fake. If one of the sides of the scale is heavier, the fake coin is on that side. Example 2. One of the nine identically looking coins is fake.
How many coins are in a fake coin stack?
If you weigh 41 coins on each scale, and it tips left or right, then you have narrowed the fake coin down to one of the 82 coins you weighed. Since 82 > 3 4, you cannot determine which is the fake coin in only four more weighings. Thus, you can weigh at most 40 coins on each scale in the first weighing.
How to narrow it down to one fake coin?
From there, continually divide 1 / 3 of that group against another 1 / 3 to narrow it down to the fake coin. If the first weighing did not balance, then you have narrowed it down to either one of he coins on the heavy pan is heavy or one of the others is light. 80 possibilities. From here, you need to narrow the possibilities down by factors of 3.
Sarah Jenkins is a veteran tech journalist with over 12 years of experience covering artificial intelligence, mobile innovations, and digital ethics. Her insights have appeared in leading technology publications worldwide.
