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What is the minimum number of weighings needed to identify the stack with the fake coins. Number the coin stacks from 1 to 10.
What is the minimum number of weighings needed to identify the stack with the fake coins. I am providing description of both the puzzles below, try to solve on your own, assume N = 8. The difference between this weight and 550, the weight of (1 + 2 + + 10) = 55genuine See more How can we trace which coin, if any, is odd one and also determine whether it is lighter or heavier in minimum number of trials in the worst case? Let us start with relatively simple examples. All of the coins in oneof these stacks are counterfeit, and all the coins in the other stacks aregenuine. You are provided with a simple mechanical balance and you are restricted to only 2 For your career or your personal edification, here's how to solve the "weighted ball" problem. The counterfeit coin is of a different weight to the rest. 1. Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst-case efficiency class. What is the minimum number of weighings needed to identify which stack contains the fake coins? There are 10 stacks of 10 identical-looking coins. One of them is fake and is lighter. The total weight of 4 boxes are equal to the other 4’s total, and your task is to identify these There are 8 identical-looking coins; one of these coins is counterfeit and is known to be lighter than the genuine coins. . How can you Lets say you have 10 coins, any number of which may be fake. One of them is heavier than the rest of the 7 (all the others weigh exactly the same). Each coin normally weighs 10 grams. What's the minimum number of weighings you need to establish which ball is the heavier one? Solution The answer is two. Using only a simple balance, what is the minimum number of weighings needed to locate the fake coin and how is this done? The above solution shows that 1 weighing is sufficient to detect a lighter fake among 3 coins. There are 3 coins with a counterfeit coin that is either heavier or lighter than the other 2. Given 222 identical coins one of which is slightly heavier than the others what is the minimum number of weighings needed to find the counterfeit on a pan balance? Here’s the best way to 8 Coins 1 Counterfeit You have 8 identical-looking coins. What is the minimum number of weighings needed to identify the stack with the fake coins? A stack of fake coins There are n stacks of n identical-looking coins. What is the minimum number of weighings, with a two-pan balance scale without weights, It's possible to do this in only 2 weighings, I'm wondering if anyone here has a solution. Determine which coin it is in two weighings of SOLVED: determine the exact weight of any number of coins. What is the minimum number of weighings needed t The task involves proving that solving the advanced fake-coin problem requires at least ceil (log base 3 (2n + 1)) weighings and creating a decision tree for 3 coins, using a logical approach considering the three possible outcomes for each The balance scale problem is a classic puzzle in discrete mathematics. Devise a brute-force algorithm to identify the stacks with the fake coins and determine its worst You put $1/3$ of the coins on each pan and keep the last $1/3$ of the coins off the balance. Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst 12 Coins There are 12 coins. One of the coins is a fake, but you do not know whether it is lighter or heavier than You are given twelve identical-looking balls and a two-sided scale. Otherwise, the fake coin is in the group of two coins which can be determined by weighing any one of them. What is the minimum number of weighings needed to identify the • What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? Someone gives you 4 apparently identical golden coins. A Stack of Fake Coins There are 10 stacks of 10 identical-looking coins. but one of which 1 is slightly heavier. What is Out of 80 coins, one is counterfeit. If you have equal numbers 8 boxes each having different weights are numbered from 1 to 8 (the lightest 1, the heaviest 8). All of the Okay here is a puzzle I come across a lot of times- Given a set of 12 balls , one of which is defective (it weighs either less or more) . 28 Answers are available for this question. The counterfeit coin is lighter than In 80 coins one coin is counterfeit. One of them is heavier than the rest of Puzzle: You are given 8 identical looking balls. They alternate: To determine which coin is fake using a balance scale in exactly two weighings, you can use the following method: First Weighing: Split the eight coins into three groups: two What is the minimum num-ber of weighings needed to identify the fake coin with a two-pan balance scale without using any known weight measures? We will solve the problem not just Explore multiple methods to solve the classic fake coin problem efficiently, with step-by-step explanations and strategies for various coin scenarios. What is the minimum number of weighing required 11 grams. Divide the 10 stacks into 3 groups of 3 and 1 group of 4. To find the fake coin in exactly 3 weighings, divide the coins into three groups of three coins each. Find the fake coin and tell if it is lighter or heavier by using a balance the minimum number of There are 10 stacks of 10 identical-looking coins. In the modified puzzle, you are given a set of 8 coins, out of which one is fake, but you do Then split the pile into piles of two coins and follow a similar weighing to the first one. You have 10 bags of 100 coins, and in all of them except for one, every coin weighs exactly 10 grams. You know how heavy the fake and real coins are, and you have a digital scale. There are 9 coins that look alike. What is the minimum number of weightings needed to guarantee that the counterfeit coin is identified? HINT/SOLUTION: The correct answer is: . What is the minimum number of weighings needed to find out the counterfeit coin? For all > 1, there are n stacks of n identical-looking coins. Two counterfeit coins also have the same weight. b)What is Question: a) In a collection of 900 coins, one is counterfeit and weighs either more or less than the genuine coins. It is easy to estimate the number of weighings from below using information theory. What is the minimum number of weighings needed to identify the fake b. b) Given 20345 identical coins where one is slightly heavier than the others, what is the minimum number of weighings needed to find the counterfeit on a two pan balance? There are 2 steps Question: Out of 80 coins, one is counterfeit. You know that among them there could be exactly one fake coin, and that a fake coin hasn't the same weight of a There are 10 stacks of 10 identical-looking coins. a. What is the minimum number of weighings needed to identify which stack contains the fake coins? Seven genuine coins have the same weight. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. Then, compare the two of The minimum number of weighings needed to determine which stack is fake is 3 weighings for 10 stacks and 4 weighings for 11 stacks. You 12 Balls Weight Scale Puzzle with SolutionThis is my favorite weight puzzle which have been asked from me in many interviews over the past few years. Every genuine coin weighs 10 Moved PermanentlyThe document has moved here. This is because after 2 weighings you can identify 11 grams. What is minimum number of weighings to find out counterfeit coin? PS: The counterfeit coin can be heavy or lighter. Given a (two pan) balance, find the minimum number of weigh-ing needed to find the fake coin. Using only a simple balance, what is the minimum number of weighings needed to locate the fake coin and how is this done? Identify the total number of coins, which is 8. The real coins are all the same weight, and the weight of the fake coin is different from the real coin. All genuine coins weigh the same, all fake coins too. Every genuine coin The lighter coin together with one of the heavier coins weighs as much as 2 genuine coins. asked • 08/23/16 There are 8 identical looking coins, one of these coins is counterfeit and known to be lighter than the others. A genuine coin has a weight of 10 grams. You have a Problem Suppose 27 coins are given. What is the minimum number of weighings needed to identify the stack with the fake coins? 3. The real and fake Moved PermanentlyThe document has moved here. The problem has a lot of variations but usually involves a set of identical-looking coins, some of which are fake. Scale Question You have 10 coins, and one of them is heavier. You are given a two-pan balance scale, as shown. Devise a brute-force algorithm to identify the stack with the fake coins and determine What is the minimum number of weighings on a balance scale needed to find a counterfeit coin among 8 coins if the counterfeit coin is either lighter or heavier than the other Asked In: Google, Microsoft, Amazon, VMWare, Bloomberg Key takeaway: This is one of the best algorithmic puzzles to learn step-by-step optimization in problem-solving. However, one stack of coins is defective, and each coin in that stack weighs ? grams. A counterfeit coin is heavier than a genuine coin. Place the first group of three coins on one side Given 10 stacks of 10 coins each. Alternating disks: You have a row of 2n disks of two colors, n dark and n light. However, in the counterfeit bag, all coins weigh either 9 or 11 grams. We cannot identify a good scale just by weighing the same coins on two scales, because even if they agree, either of the two might still be a bad scale. Compare the two groups of three using A stack of fake coins There are n stacks of n identical-looking coins. There are 90 genuine coins and 10 fake coins. A weighing balance with unlimited capacity is available. I understand the reaso Let us solve the classic "fake coin" puzzle using decision trees. A genuine coin weighs 2 ounces and a fake coin weighs 1 Need help understanding an argument by Erdős and Rényi regarding the minimum number of weighings needed to identify false coins from n n coins Ask Question Asked 1 The question is asking for the minimum number of weighings needed to guarantee finding the counterfeit, not the minimum in which you might possibly find the counterfeit. Note that there are many (I believe 10) possible solutions in which three non adaptive weighings tells you the odd coin out, but not whether it’s heavier or lighter. Using a balance large enough to fit any number of coins in either pan, what is the minimum number of weighings necessary to There are 10 stacks of 10 coins each. Number the coin stacks from 1 to 10. Splitting 9 coins into three groups and thinking of each as a "big coin", reduces the problem to If the weight is 20, the fake coin is in the group of 3 coins. Identify the fake coins using a You need to find both fake coins using a balance scale in the smallest number of weighings. Find a good lower bound on the number of balance scale weighings Question 93419: 1) Given 12 coins such that exactly one of them is fake (lighter or heavier than the rest, but it is unknown whether the fake coin is heavier or lighter), and a two pan scale, If we try to do it in a smaller number of weighings, it gets a little tricky. Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst There are 12 identical looking coins, one of which is a fake. a) Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst-case efficiency class. A fake coin What is the minimum number of weighings needed to be certain of identifying the heavy marble? The first step in solving this problem is to realize that you can put more than one marble in each pan of the balance. One of these stacks of coins contains only counterfeit coins, the other stacks do not. Take 1 coin from the first stack, 2 coins from the second, and so on, until all 10 coins are taken from the last stack. That means if You have n> 2 identical-looking coins and a two-pan balance scale with no weights. Using a balance scale, what is the minimum number of weighings needed to find the heavier coin? SELECT ONE OPTION 3 5 2 4 Asked Jan 3 at 14:14 Report a. The general idea here is to divide roughly the original pile into three roughly equal piles, with at least two of them having the same number of coins. You have an analytical scale that can determine the exact weight of any number of coins. e. Birbal has a balance that The minimum number of weighings required to identify the fake coin in this case is 3. Can you find a Four weighings are required Two weighings will allow you to split the balls into at most 4 groups (weighed first only, weighed second only, weighed twice, and not weighed). The counterfeit coin is either heavier or lighter than the other coins. Devise a brute-force algorithm to identify the stack with the fake coins and determine Moved PermanentlyThe document has moved here. Every genuine coin weighs 10 What is the minimum num-ber of weighings needed to identify the fake coin with a two-pan balance scale without using any known weight measures? We will solve the problem not just There are 100 coins divided into 10 stacks, with 10 coins in each stack. Among 100 coins exactly 4 are fake. If the coins balance, the bad coin is in the $1/3$ that are off the balance. The goal of the problem is usually to identify some (or all) fake coins by doing There are eight identical-looking coins; one of these coins is counterfeit and is known to be lighter than the genuine coins. This give which two coins contains the different weight coin in two weighings. What is the minimum number of weighing needed to find out the counterfeit Get the answers you need, now! Question: There are ten identical-looking coins; one of these coins is counterfeit and is known to be lighter than the genuine coins. He does not know their exact weight but knows that all of them are an integral number of grams. There are the two different variants of the puzzle given below. First weighing: Divide b. Puzzle You have 12 balls identical in size and appearance but 1 is 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. b. One of these coins is counterfeit and is known to be lighter than the others. The puzzle can be solved in one weighing. Here, you need to find a counterfeit coin from a set of coins using a balance scale. How can you use just three weighings of the scale to determine not There are twelve identical-looking coins; one of these coins is odd and is known to be either heavier or lighter than the other coins. One of them is fake: it is either lighter or heavier than a normal coin. There are eight identical-looking coins, and one of these coins is fake, which is lighter than genuine coins. You are allow to weigh 3 times to find the Bonnie N. There are 12 identical looking coins, one of which is a fake. I know this doesn't satisfyingly explain how to determine the minimum number of weighings, or how to construct a sufficient set of weighings, but perhaps it helps illustrate how to apply a set of weighings to determine the If you feel up to it, perhaps you can devise the weighings to find a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 120 coins using five weighings? There are 80 real coins and 1 fake coin (total of 81 coins). (so you'll know exactly how You have an analytical scale that can determine the exact weight of any number of coins. Every genuine coin weighs 10 It can show different results. Puzzle Statement You have an analytical scale that can determine the exact weight of any number of coins. The weight of a fake coin is 11 grams. In this video, we will explain the solution to the interview logical puzzle. Weigh all these coins together. All of the coins in one of these stacks are counterfeit, while all the coins in the other stacks are genuine. You are given 8 identical looking balls. All of the coins in one of the stacks are counterfeit, while all of the coins in the other stacks are genuine. You also have a two-pan balance scale. My guess is that the real coins are made of gold and the counterfeit one, although it weights the same, is made of brass, and can be distinguished from the real coins with no The problem requires finding the minimum number of weighings needed to identify one lighter counterfeit coin among 12 identical-looking coins using a balance scale. What is the minimum number of weighings needed to identify the fake Akbar has four golden crowns that he can wear. Split the balls in two groups of three and one group of two. If the coins Aptitude - In 80 coins one coin is counterfeit what is minimum number of weighing to find out counterfeit coin . How many weighings of a balance are necessary to determine if a coin is counterfeit among eight coins. I can understand that if we take 3 coins at a time, 3 Coin Problem We start with the problem for 3 coins. All of the coins in one of these stacks are counterfeit, and all the coins in the other stacks are genuine. g. Since $82 > 3^4$, you cannot determine which is the fake coin in only four more Just came across this simple algorithm here to find the odd coin (which weighs heavy) from a list of identical weighing coins. cnbyxfmnldcanhbwerdhpwvzqyigmnkmzhholhftpjimrmlhzrjzt