The Counterfeit Coins Problem is a well-known complex search problem in mathematics as well as in computer science. It can be related to the data structure (such as binary tree) computer program, algorithm, Graph Theory, Therefore researching this problem is meaningful. The Counterfeit Coins problem can be described as given a set of n look-alike Coins containing One Counterfeit which is a bit heavier or lighter than the genuine Coins. The objective is to find the Counterfeit Coins in minimum numbers of weighing w (trials) with a simple arm balance scale. While a balance scale provides information about the Counterfeit Coins by comparing the weights of the two subsets of Coins, we can also detect Counterfeit Coins by a spring scale which provides
…show more content…
Along with it may be given one or many true (or genuine) Coins. Our problem is a distinctive case of the Counterfeit Coins problem where we are given eight Coins and we know that one of the Coins is false and distinguishable by weight. This algorithm is based on the existing classical solution of a more formal instance of this problem, known as the Eight Coins Problem, where there eight Coins are given among which only one Coin is false. The solution is shown in Figure 1, which is a decision tree. The tree in this figure represents a set of decisions by which we can get the solution of our problem. We use H or L as a suffix to represent the Counterfeit (or false) Coins as heavier or lighter, respectively. In the solution of the eight Coins problem in the form of a decision tree in Figure 1, each internal vertex (other than leaf vertices) represents a comparison between a pair of sets of Coins using an equal arm …show more content…
The objective is to find out the false Coins using a minimum number of comparisons amongst the Coins and also to determine the characteristic feature of the false Coins whether it is heavier or lighter in comparison to each of the true Coins. Now the question is what the minimum number of comparison is required since the each Coins has the two possibility heaver and lighter, so the total possibility is 16, if we consider w is the total number of comparison then, w=log_316≅3 Twelve Coins Problem
There is piles of twelve Coins all of equal size. Elevens are of equal weight. One is a different weight. In three weighing find the Counterfeit Coins and also determine the characteristic feather of the Counterfeit Coins whether it is heavier or lighter in comparison to each true
Along with it may be given one or many true (or genuine) Coins. Our problem is a distinctive case of the Counterfeit Coins problem where we are given eight Coins and we know that one of the Coins is false and distinguishable by weight. This algorithm is based on the existing classical solution of a more formal instance of this problem, known as the Eight Coins Problem, where there eight Coins are given among which only one Coin is false. The solution is shown in Figure 1, which is a decision tree. The tree in this figure represents a set of decisions by which we can get the solution of our problem. We use H or L as a suffix to represent the Counterfeit (or false) Coins as heavier or lighter, respectively. In the solution of the eight Coins problem in the form of a decision tree in Figure 1, each internal vertex (other than leaf vertices) represents a comparison between a pair of sets of Coins using an equal arm …show more content…
The objective is to find out the false Coins using a minimum number of comparisons amongst the Coins and also to determine the characteristic feature of the false Coins whether it is heavier or lighter in comparison to each of the true Coins. Now the question is what the minimum number of comparison is required since the each Coins has the two possibility heaver and lighter, so the total possibility is 16, if we consider w is the total number of comparison then, w=log_316≅3 Twelve Coins Problem
There is piles of twelve Coins all of equal size. Elevens are of equal weight. One is a different weight. In three weighing find the Counterfeit Coins and also determine the characteristic feather of the Counterfeit Coins whether it is heavier or lighter in comparison to each true