How do you solve fake coin problems?
How do you solve fake coin problems?
If two coins are given, put one coin on each pan. The higher pan contains the fake lighter coin. If 3 coins are given and one among them is known to be a fake lighter coin, put one coin on each pan and leave the third coin aside. If the pans balance, then the third coin is the lighter fake coin.
Can you find the counterfeit coin using just two weighings?
Solution 1 Take any two of them and put them on the opposite cups of the scale. If they weigh the same, it is the third coin in the lighter group that is fake; if they do not weigh the same, the lighter one is the fake. Thus the problem is solvable in two weighings.
What is the minimum number of weighings needed to find the fake coin?
By the way, two weighings is the smallest number of weighings that guar- antee finding the fake coin. In addition, 9 is the largest number of coins such that the fake coin can be found in two weighings.
Can you solve the counterfeit coin riddle answer?
Take two of those three coins and weigh them against each other. If the balance tips then the lighter coin is the odd one out. If the two coins balance then the third coin not on the balance is the odd one out and it is lighter.
Can coins be fake?
Coin counterfeiting of valuable antique coins is common; modern high-value coins are also counterfeited and circulated. Counterfeit antique coins are generally made to a very high standard so that they can deceive experts. This is not easy and many coins still stand out.
Which is the lightest coin?
But there are always exceptions. And no single object is a greater exception than the Nepalese silver ¼ Jawa, which was minted circa 1740 and remains the smallest and lightest coin ever made.
How do you find the heavier coin?
two weighings are needed. separate into three groups (3,3,2) put three on each side of scale, if sides balance then place two remaining coins on either side of scale to see which is heavier.
Why is counterfeit money so hard?
Because everything from the paper to the ink to the printers required to reproduce a high quality counterfeit is nearly impossible to obtain either because of price or exclusive contracts on production of those materials.
How can you tell if a coin is a fake?
First weighing: three coins aside, three on each side of the scale. This way you will determine three coins which have a fake coin among them. Second weighing: Problem 1. Example 3. One of the 27 identically looking coins is fake. It is known that the fake coin is heavier than the other 26.
How to reduce problem space for fake coin?
Both sides have identical weight: the fake coin cannot be in the two stacks weighed, so must be in the 3rd: you reduced the problem space to 1/3 2.) One side weighs more than the other: since there is only one fake coin it must be on the side that weighs less: again you reduced the problem space to 1/3 Rinse and repeat.
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.
Is there an algorithm for the fake coin problem?
Classic problem with 12 coins ( or marbles) one of which is fake. Fake coin assumed to be lighter than real one. Having scales to compare coins (or marbles). One can do comparison one by one and compare all 12 coins. More efficiently one can do it using Decrease By Factor algorithm.