The general counterfeit coin problem

نویسندگان

  • Lorenz Halbeisen
  • Norbert Hungerbühler
چکیده

Given c nickels among which there may be a counterfeit coin, which can only be told apart by its weight being di erent from the others, and moreover b balances. What is the minimal number of weighings to decide whether there is a counterfeit nickel, if so which one it is and whether it is heavier or lighter than a genuine nickel. We give an answer to this question for sequential and nonsequential strategies and we will consider the problem of more than one counterfeit coins.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Optimal non-adaptive solutions for the counterfeit coin problem

We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists, (iii) we have access to additional genuine coins, and (iv) we need to determine if the counterfeit coin is heavier or lighter than the genuine ones. Moreover, ou...

متن کامل

An Advanced Approach to Solve two Counterfeit Coins Problem

Though the counterfeit coin problem is well known as a fascinating puzzle it claims great importance in Computer science, Game theory, and Mathematics. In terms of the puzzle the objective is to detect the counterfeit coins which are identical in appearance but different in weight. The word counterfeit not only describes forgeries of currency or documents, but can also be applied to software, p...

متن کامل

Optimal Algorithms for the Coin Weighing Problem with a Spring Scale

Suppose we are given n coins out of a collection of coins of two distinct weights w0 and w1, true and counterfeit coins, respectively, where d of them are counterfeit coins. Assume we are allowed to weigh subsets of coins in a spring scale. Determine the counterfeit coins in a minimal number of weighing. This problem is equivalent to the following learning problem: Given a linear function f = x...

متن کامل

Solution to the Counterfeit Coin Problem and its Generalization

This work deals with a classic problem: ”Given a set of coins among which there is a counterfeit coin of a different weight, find this counterfeit coin using ordinary balance scales, with the minimum number of weighings possible, and indicate whether it weighs less or more than the rest”. The method proposed here not only calculates the minimum number of weighings necessary, but also indicates ...

متن کامل

SNIEDOVICH OR/MS Games: 3. Counterfeit Coin Problem OR/MS Games: 3. Counterfeit Coin Problem

In this discussion we examine two versions of the famous Counterfeit Coin Problem, focusing on their educational OR/MS content. It is shown that this problem provides an excellent environment for illustrating a number of fundamental OR/MS problem-solving concepts and methods related to decision making under uncertainty. A number of interactive modules are provided for experimentation with this ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Discrete Mathematics

دوره 147  شماره 

صفحات  -

تاریخ انتشار 1995