27 coins and a two pan balance There is a sensitive two-pan balance (without any weights). May 31, 2023 · Coin Weighing Suppose that one has n coins, among which there may or may not be one counterfeit coin. The single-pan balance was invented in the 1950s and saw widespread use. They tell us each bag has x coins and we have to find x. Aug 26, 2020 · Puzzle 1: One of twelve coins is a bit lighter than the other 11 (which have the same weight). Using a two pan balance, the goal is to determine with certainty the fake coin, and whether it is lighter or heavier than a genuine coin. Peter has a two-pan pointer scale which shows the difference in weights between A druggist has the five weights of 1,3,9,27, and 81 ounces, and a two-pan balance. , either heavier or lighter than the other coins). Feb 28, 2022 · Difficult: Given a two pan fair balance and N identically looking coins out of which only one coin may be defective. Participants outline various strategies to identify the odd coin and determine its weight difference. The counterfeit coin is either heavier or lighter than the other coins. There are ten identical - looking coins; one of We have bags of coins and loose coins on a two-pan balance. The balance has sensitivity su cient for the task. Each side of the balance represents one side of the equation. What does the pan scale measure? A double-pan balance can also be used to determine how much of a substance makes up a specified weight. 3 Mathematical Analysis of Nonrecursive Algorithms 61 11. Assuming that he has a two pan scale. logical-deduction weighing Mike Earnest 32. ) There are various ways in which we can solve this puzzle. The first weighing clarifies if the suspected coins balance or identify a potential fake coin, leading to further analysis in May 28, 2015 · Inspired by this puzzle You have $121$ apparently identical gold coins. Among them are two fake coins. Step 3/8If one group is heavier, divide that group into two equal groups of 55 coins each. Provide a strategy to detect the fake coin with the minimum number of weighings. Each time you use the scale, there are 3 possible outcomes LCR (left weighs less than right), as shown here L= R (left and You are also given a two-pan balance to use. Today, modern laboratories use electronic balances. What is the Mar 11, 2021 · Detective Mike has four bags with 100 coins of one cent each. You have n > 2 identical-looking coins and a two-pan balance scale with no weights. In Dickens’s time, merchants measured many commodities using weights and a two-pan balance – a practice that continues in many parts of the world today. Taking the 27 coins from that bag, clear the other coins from the balance and use Method A to find the odd coin in the 3 remaining weighings. Let's say you label them A, B, and C. One of them is fake and is lighter. One of the coins is fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same. If they balance, the third pair of coins is faulty. How can you generalize this result? | Numerade We're recalculating the answer now 1% We would like to show you a description here but the site won’t allow us. Of 101 coins, 50 are counterfeit. Nov 3, 2015 · There are 27 coins and a two-pan balance. You have a two-pan balance. The double-pan balance scale is an There are eight identical-looking coins; one of these coins is counterfeit and is known to be lighter than the genuine coins. 57 and 2. At most how many times must I use one or the other, or both, to determine the two fake coins? Apr 9, 2022 · What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? You have a pile of 8 identical coins, and you know one of them is fake and is lighter than the genuine coins. You compare two of the groups on the scale, and this will tell you if the fake coin is there—if the scale tips, you’ve got it narrowed down. The context—weighing a set of coins in order to identify the one coin that weighs less than the others—allows students to manipulate the weight on either side of the scale. You are given 27 coins and a balance scale. (a) Find an upper bound on the number of coins n so that k weighings will find the counterfeit coin (if any) and correctly declare it to be heavier or lighter. Balances come in many forms from simple to sophisticated. The weight of one genuine coin is an unknown integer, while all the counterfeit coins have the same weight that differs from the weight of a genuine coin by 1 gram. 12. You are only allowed 3 weighings on a two-pan balance and must also determine if the counterfeit coin is heavy or light. What is the minimum number of weighings that will ensure identification of the dummy coin using a two-pan balance? Jun 27, 2022 · Balance-scale puzzles abound in recreational mathematics. What is the minimum number of weighing required to certainly find out heavier coin? 1 C language and Current affairs Divide the coins into three groups 9 each weigh them odd 9 coins will be Jan 29, 2014 · There are 27 coins and a two-pan balance. This proposal assumes that a person is able to discern the weight diference between a genuine coin and the counterfeit. If the two pans balance, then the false coin must be in the group of 22. Question: Lighter or heavier? You have n > 2 identical-looking coins and a two-pan balance scale with no weights. Question: You have n > 2 identical-looking coins and a two-pan balance scale with no weights. The coins are to be weighed by a balance. one of the coins is a fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same. How would you identify this lighter coin if you could use a two-pan balance scale only 3 times? (You can only balance one set of balls against another i. And how is this possible? Jul 25, 2025 · Given 27 coins with one lighter (dummy) coin, we need to find it using a two-pan balance in the minimum possible number of weighings. May 24, 2025 · Suppose that among n identical-looking coins, one is fake. Scale 2What is the minimum number of weightings needed to guarantee that you will identify the fake coin? You may place more than 1 coin on each pan at a time. you have no weight measurements. If the two coins tested weigh the same, then the lighter coin must be one of those not on the balance. 5, respectively. Math Advanced Math Advanced Math questions and answers 3. 1 Version 1 (Type Known) There are 12 otherwise identical coins, except that one of these coins is a counterfeit and it is known to be lighter than the genuine coins. m. The discussion centers on a problem involving 120 visually identical coins, where one coin is either heavier or lighter than the rest. Number the coins 1, 2 and 3. A weighing consists of putting a sample of coins on each pan of the balance and observing whether the pans balance or whether one pan weighs more than the other pan. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. The mission is to identify the counterfeit coin - with the aid of a two-pan balance - deploying the smallest possible number of weighings. In each use of the balance you may put any number of the 4 balls on the left pan, and the same number on the right pan, and push a button to initiate the weighing; there are three possible outcomes: either the weights are equal, or the balls on the left are heavier, or the balls on the left are lighter. All genuine coins weigh the same. Weigh two May 28, 2015 · Inspired by this puzzle You have $121$ apparently identical gold coins. What is the minimum number of weighings needed t We can only use a two-pn balance scale Follow 2 Add comment More Report you have n> 2 identical-looking coins and a two-pan balance scale with no weights. One of these coins is counterfeit and is known to be lighter than the genuine coins. You have n>2 identical-looking coins and a two-pan balance scale with no weights. Feb 14, 2023 · You weigh these two coins if they are the same then the left coin in the 3-coin-pile is the fake one and if they do not weigh the same then the lighter one is the fake one. Mar 22, 2022 · Consider a set of 101 coins, of which 50 are counterfeit. Jan 15, 2013 · From these ancient times until the 1950's laboratories used two-pan balances to determine weight. A smart solution is to split the coins into three groups. What is the least amount of times that you have to use the scale to ensure you find the counterfeit coin. If you are using a limited set of weights, however, you can only measure certain quantities accurately. Otherwise, the pan with the faulty coin will remain on top. Design a O (1) algorithm to determine whether the fake coin is lighter or heavier than the othersplease show your work Question: 11. A detailed method is proposed, involving systematic weighings and logical deductions based on the outcomes of each weighing 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, devise a procedure to identify the fake coin and whether it is heavier or lighter by doing no more than 3 weighings. All coins looks identical. Weight is a force exerted upon an object by gravity while mass is the quantity of matter in an object. Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Jan 26, 2019 · It has a balanced beam and two pans. 9) from the wonderful collection Mathematical Circles (Russian Experience). The essential element is the humble two-pan balance scale — a staple of commerce over the millennia that’s still found in bustling rural bazaars in the developing world. All the coins visually appear the same, and the difference in weight is imperceptible to your senses. With One Weighing Here's problem 31 (p. Design an algorithm to determine whether the fake coin is lighter or heavier than the others. I understand the reaso Problem 2: You are given twelve coins that are identical in appearance. The simplest versions consist of a metal beam from which hang two pans at equal distances from the central support or fulcrum. To find the lighter coin among 7 coins using a two-pan balance, a decision tree involves multiple weighings. You can weigh coins on a two-pan balance scale. Oct 16, 2022 · The riddle There are 12 coins, all identical in appearance. 18 of those coins have a weight of 10g each, 1 coin has 9g and 1 coin has 11g. What is the minimum number of weightings needed to identify the fake coin with a two-pan balance scale without weights? anikam Expert Asked on 22nd August 2015 in Interview Puzzles. You have a two-pan balance scale without weights. Design a θ (1) algorithm *****WITH PYTHON CODE***** to determine whether the fake coin is lighter or heavier than the others. Question: There are ten identical-looking coins; one of these coins is counterfeit and is known to be lighter than the genuine coins. design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. If one pan dips, then the false coin must be in that pan. What is the minimum number of weighing required to certainly find out heavier coin? javarevisited. 2 12 pts) You have n > 2 identical-looking coins and a two-pan balance scale with no weights. A much simpler pan-balance puzzle asks how to weight any object from 1 to 31 kg using the powers of two as weights: 1, 2, 4, 8, 16 kg. A two-pan balance scale is used to identify a counterfeit coin via weight comparisons. Each weighing would result in one of three outcomes: < means lighter in weight, = means equal in weight, and > means heavier in To solve this in only four weighings, Divide the coins into groups of 21, 21, and 22 coins. May 19, 2023 · #12 #12 E 2. Claim: 5 weighings are needed to find the counterfeit coin on a pan balance. Aug 11, 2020 · You have n> 2 identical-looking coins and a two-pan balance scale with no weights. Weight is different at different locations while mass always stays Moved PermanentlyThe document has moved here. Coins #1 You have a number of gold coins of the same denomination. In front of you is balance with two pans. Weight is different at different locations while mass always stays Jan 1, 2020 · You are given 20 identical coins. Lighter or heavier? You have n>2 identical-looking coins and a two-pan balance scale with no weights. The simplest version consists of a metal beam that hangs two pans at the same distance. Dec 16, 2013 · There are 27 coins and a two-pan balance. All the coins weigh the same amount except one coin is counterfeit and weights slightly less. The two-pan balance scale is an important part of rural bazaars in the developing world. Jun 27, 2022 · There are balance-scale puzzles in math. You are allowed to weigh coins using a two-pan equal-arm balance (sometimes called a scale or scales), as shown in figure~1. Jun 23, 2025 · A lot has 27 similar coins, of which exactly one is defective (i. To identify the fake coin among n identical-looking coins, where one coin is either heavier or lighter, you can use the following algorithm which involves a two-pan balance scale: Step 1: Group the Coins Divide the n coins into three groups as evenly as possible. You believe that all of the coins are genuine, but it is possible that one coin is a fake. In doing so, they are focused on the relationship between two weights—two quantities—and whether or not they are equal. (b There are 8 identical coins. You can place an object in one pan and standard weights in the other to find what the object weighs. Feb 16, 2023 · 12 I have twenty-four identical-looking coins, but two are fake and weigh possibly different from each other, though definitely different from the remaining genuine coins. To find the lighter one we can compare any two coins, leaving the third out. At most one of these is fake, and weighs a different amount than a genuine coin. Oct 16, 2020 · With a two-pan balance, isolate the counterfeit coin in three weighings. Oct 25, 2023 · Step 1/8Divide the 222 coins into two equal groups of 111 coins each. How many weigh trials at minimum has had to make to find with certainty the false coin? Four coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. 1. Divide the defective nine-piece set into three sets of triplets. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. e. 4k asked May 27, 2015 at 16:21 6votes 2answers 197kviews The maximum number possible is three. Just put the number without any decimal places. Design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. I have a weighing scale and a two-pan balance. The two sides are EQUAL (weigh the same). What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? You have 9 silver dollars — 8 genuine and 1 fake (it is heavier than the others) — and an accurate "two pan balance" (with the fulcrum in the middle of a meter stick, with everything symmetric) that lets you distinguish between real and fake coins. For example, if one pan weighs 158 grams and the other weighs 136 grams, the reading would be 22 Aug 23, 2016 · There are 8 identical looking coins, one of these coins is counterfeit and known to be lighter than the others. On the left balance pan there are 3 bags and 17 loose coins . One coin, however, is counterfeit, having a slightly different weight than the other N-1 coins. Determine the counterfeit coin using a balancing scale with the least number of tests. All the real coins weigh the same, but the fake coin weighs less than the rest. For n = 3 coins, the decision tree uses two weighings to identify the fake coin and its weight status. Lighter or heavier? You have n > 2 identical-looking coins and a two-pan balance scale with no weights. Details concerning this standard version of the problem can be found in Albers (1966) and Martelli and Gannon 1. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. One of the coins is a fake, but you do not know whether it is lighter or Answer or Resolution People have come up with clever methods to solve the Counterfeit Coin Problem. Sep 8, 2023 · You have 27 coins and a balance scale, and one of the coins is fake. Question: Suppose you have 5 coins, one of which is counterfeit (either heavier or lighter than the other four). Question: You have n > 2 identical-looking coins and a two-pan balancescale with no weights. Question: You have n>2 identical-looking coins and a two-pan balance scale with no weights. (You use a pan balance scale to find the bad coin and determine whether it is heavier or lighter. The minimum number of weighings required in the worst case is 3. What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? Write out your algorithm. Compare the weights of two of these piles using the pan balance. Group the 222 coins into 3 piles of 74 coins each. Show that he can weigh any integral amount up to and including 121 ounces. Question: How do you find the light counterfeit coin among eight coins in two weighings? Assume that a balance scale is used and that all coins in question have identical appearance. Design (1) algorithm to determine whether the fake coin is ligher or heavier than the Apr 12, 2001 · At one point, it was known as the Counterfeit Coin Problem: Find a single counterfeit coin among 12 coins, knowing only that the counterfeit coin has a weight which differs from that of a good coin. When the pans contain exactly the same mass the beam is in balance. I give you a bag containing 27 coins, which look exactly the same. Feb. Design a O (1) algorithm to determinewhether the fake coin is lighter or heavier than the others. In front of you is balance with two pan 121 coins and a balance Inspired by this puzzle You have $121$ apparently identical gold coins. 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? A balance puzzle or weighing puzzle is a logic puzzle about balancing items—often coins—to determine which one has different weight than the rest, by using balance scales a limited number of times. 24, 2022 04:19 a. We start with the problem for 3 coins. Goals and Learning Objectives Nov 16, 2015 · How many weighings of a balance are necessary to determine if a coin is counterfeit among eight coins. If it has not changed, rotate the bags of 9 coins and observe the condition of the balance. Jun 28, 2015 · This is an extension of a previous three-pan balance puzzle. Aug 14, 2008 · The discussion centers around solving a classic puzzle involving 12 coins, where one is either heavier or lighter than the others, using a balance scale only three times. On the first weighing, place coin 1 on the left pan and coin 2 on the right pan. Given a (two pan) balance, find the minimum number of weigh-ing needed to find the fake coin. You have a pan balance, but you have only enough time to make 3 weighings. [Problem 11 - Exercises 2. 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? Nov 16, 2015 · How many weighings of a balance are necessary to determine if a coin is counterfeit among eight coins. In front of you is balance with two pan The maximum number possible is three. To find the triplet containing the defective coin, repeat step 2 above. Step 2/8Weigh the two groups on the pan balance. Engineering Computer Science Computer Science questions and answers 3. Design a Big Theta (1) algorithm to determine whether the fake coin is lighter or heavier than the others. What is the minimum number of weighing required to certainly find out heavier coin? All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. Find the Fake among 12 balls in 3 weighs. Otherwise, it is the one indicated as lighter by the balance. (for Instructor) You have a set of coins that contains at most one fake coin that is either heavier or lighter than the all rest, which are identical. Step 4/8Weigh the two groups of 55 coins. (Note: The scale in this problem is a balance scale with two Lighter or heavier? You have n > 2 identical-looking coins and a two-pan balance scale with no weights. The second problem is often referred to as the counterfeit coin problem and it is a classical puzzle. Step 5/8If one group is heavier, divide that group into two equal groups of 27 coins each. Each counterfeit coin weighs exactly 1 gram less than each normal coin. blogspot. : r/puzzles Go to puzzles r/puzzles r/puzzles There are 12 identical-looking coins. What is the minimum number of weighings that will ensure identification of the dummy coin using a two-pan balance? Preface. Take the group with the heavier coin and split into 3 groups: 7, 7, and 8 (or 7). We do not know whether the fake coin is lighter or heavier than the genuine ones. Science and art use the double-pan balance scale. A set of 27 similar looking coins has 26 identical coins and one dummy coin having less weight. The counterfeit coin is heavier than the gu rantee identification of one heavy counterfeit coin among 27 coins which are identical in appea Jul 1, 2008 · We aim to find the counterfeit nickel in three weightings using a two-pan balance. All of these coins have the weight with the exception of one coin which weighs a little less than the rest because it is counterfeited. These may be adjusted to fine-tune the balancing arms. At each weighing, we can divide the coins into three groups and use a balance to eliminate two-thirds of the possibilities at every step, since: A set of 27 similar looking coins has 26 identical coins and one dummy coin having less weight. You are given a two-pan balance scale, as shown. On the right pan there are 14 bags and 6 loose Jul 23, 2022 · We have a balance that lets us directly compare the weights of any two sets of coins from the collection, by placing them in the two pans of the balance and seeing whether one side drops, proving it to be heavier, or whether the pans remain level, proving that they contain equal weights. What is the minimum number of weighing attempts required to certainly find out heavier coin? 1 2 comments Like Comment Most relevant Gowthami GV 5 8y Naveen Navee 6 8y To determine the maximum number of identical coins that can be tested with a two-pan balance to identify one counterfeit coin (which is heavier) using w weighings, we can apply a strategy related to powers of 3. This problem is fairly simple to solve, since there is not much that we can do. The Jan 20, 2023 · Finding a fake coin out of a number of genuine coins that are presumed to be heavier than the false coins using just a balancing scale that can be used to compare the **weights **of two heaps of coins is an interesting problem called the fake coin problem. I understand the reaso The advanced fake-coin problem requires at least ⌈log3(2n + 1)⌉ weighings in the worst case to differentiate between the possibilities of genuine and fake coins. Peter has a scale in form of balance which shows the difference in weights between the objects placed in e Aug 17, 2018 · Using only a two-pan weighing balance, we weigh subsets of coins sequentially in order to identify the counterfeit coin (or declare that all coins are genuine) using the fewest weighings on average. Details concerning this standard version of the problem can be found in Albers (1966) and Martelli and Gannon Lots of Gold Stacks and a Balance Scale You are given X amount of stacks of golden coins, each stack consisting of ten (10) golden coins and a digital balance scale with perfect precision that shows how much difference between weights you 1. ) Objective To learn to use an electronic balance to make mass measurements, to determine the masses of two diferent objects, and to investigate mass loss resulting from a transfer of liquid from one container to another. You have a scale - balance type with 2 trays - but can only load it twice. You are given a traditional balance scale with two pans (no reading). Now, imagine the nine coins in three stacks of three coins each. Submitted by Tammy S. With a balance scale, we can compare any two sets of coins to determine whether the two sets weigh the same, or which of the two sets is heavier, but not by how much. 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? Test one of the 2 coins against any other coin; if they balance, the odd coin is the last untested coin, if they do not balance, the odd coin is the current test coin. . Jan 4, 2025 · Lighter or Heavier? You have n > 2 identical looking coins and a two pan balance scale with no weights. The bags are made of a very light material, much, much lighter than the coins, so the bags' weight can be disregarded. Draw a decision tree that gives an algorithm that identifies in at most two weighings the bad coin (but not necessarily determines whether it is heavier or lighter than the others) using only a pan balance. Problem Suppose 27 coins are given. The expected path length (EPL) and average weighings are approximately 2. Note 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, devise a procedure to identify the fake coin and whether it is heavier or lighter by doing no more than 3 weighings. It is the basis of the concept Question: You have n>2 identical-looking coins and a two-pan balancescalewithnoweights. Oneofthecoinsisafake,butyoudonotknow whether it is lighter or heavier than the genuine coins, which all weigh the same. How can you You are allowed to weigh coins using a two-pan equal-arm balance (sometimes called a scale or scales), as shown in gure 1. Either all of them are genuine or exactly one of them is fake. Determine which coin it is in two weighings of a balance scale. All coins has same weight except for one, which is heavier than all others. One of these coins is counterfeit and is known to be lighter than the genuine coins. Genuine coins all weight 10 grams, but a fake coin will weigh either 9 or 11 grams. Peter has a two-pan pointer scale which shows the difference in weights between Feb 14, 2023 · You weigh these two coins if they are the same then the left coin in the 3-coin-pile is the fake one and if they do not weigh the same then the lighter one is the fake one. May 14, 2018 · Of $101$ coins, $50$ are counterfeit, and differ from genuine coins in weight by $1$ gram. We would like to show you a description here but the site won’t allow us. A balance should have small sliding compensators on either side of the fulcrum (pivot point). The balance has sensitivity sufficient for the task. If there is a counterfeit coin, it may be either heavier or lighter than the other coins. Twenty-six coins weigh the same and one counterfeit coin weighs less than the others. Modeling equations with a pan balance: video lessons In the first video, I explain the basics of how we model simple equations with a pan balance (scales). Some buckets will come with lids, pouring spouts and calibrated scales on the side. Use the prune-and-search strategy to design an efficient algorithm for detecting the fake coin. Justification: Step 1: The 222 coins can first be grouped into 3 piles each of 74 coins (74 x 3 = 222) The first two piles can be compared using the balance. One of the coins is a fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same. Whenever one can deduce that one or more coins are genuine, they will be inmediately discarded and may no longer be used in subsequent weighings. Weigh two of them separately. All 12 Balls look same and you have a pan balance with no weights. However, there is 1 fake coin, which is either heavier or lighter than the remaining coins. Apr 2, 2018 · Divide the 27 coins into three groups of nine coins each. Design an algorithm to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. Jul 8, 2020 · • What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? Jan 27, 2019 · This sounds like the balance could never be balanced, but the 3-pan balance is an example which fulfills this criterion and is still balanced (if all coins are equal). Participants explore strategies to identify the odd coin using a two-pan balance within five weighings. There are 3 coins with a counterfeit coin that is either heavier or lighter than the other 2. You have a weighing balance with two pans that gives the difference between the weights of the two pans as an outcome. Most balances come with a bucket on either side that allows students to weigh objects or liquids. What is the minimum number of weighings needed to identify the fake coin with a two-pan balance scale without weights? The answer is an integer . The balance provides one of three possible indications: the right pan is heavier, or the pans are in balance, or the left pan is heavier. com Top 10 Puzzles, Riddles, Logical and Lateral Thinking questions asked in Programming Job Mar 7, 2015 · There are 27 coins and a two-pan balance. Problem Suppose 27 coins are given. ns are identical in appearance, but one is counterfeit. Weigh the two groups of 21. Two-pan balance and generalized counterfeit coin problem Marcel Kołodziejczyk Hugo Steinhaus in „Mathematical Snapshots” ([7]) offers the following problems: We have nine nickels, including one counterfeit coin, which can only be told apart by its weight being different from the others. Jul 29, 2022 · Readers balanced logical reasoning and mathematical insights to find phony coins with a double-pan balance scale. One of the coins is a fake, but you do not know whether is is lighter or heavier than the genuine coins, which all weight the same. Some students said they would first use their hands (a two-pan balance of sorts!) to compare coins until the heavier counterfeit coin had been identified, and then confirm the identification with the two-pan balance. qnjxko jjnwy fisai pjis emh gesbcc ncmvct ynwbl jdql keg uslbp fewhb dajrvio pbmt suwxj