You have nine identical coins of which 8 have the same weight. But you only have more coins to assign.

7 of the eight balls are equal in weight and one of the eight given balls is defective and weighs less. Explain how this can be done. In addition, you have a $15$ th coin that is known to be good. i) they weigh the same, weigh 12/4 to see if 12 is lighter or heavier. 10 coins from the tenth bag and simply weigh the picked coins together ! If there were no forgeries, you know that the total weight should be (1+2+3+ . The task is to find the defective ball in exactly two measurements. The heavier group should then be obvious, it will either tip the scales, or, if the scales stay balanced, then it is the group you didn't include. You have a balance, with which you can compare two sets of coins A and B, to determine whether A is heavier, B is heavier, or they weigh the same. Among the nine, eight coins are genuine and weigh the same whereas one is a fake, which weighs less than a genuine coin. But actually some of them are pure gold coins (hence are heavy) and the rest are aluminum coins with thin gold plating (light). A you can tell whether it is lighter or heavier. Dec 31, 2018 · Let’s name those remaining coins as A, B, C. Question: 6. Question: Suppose you have eight coins, one of which is counterfeit (either heavier or lighter than the other seven). Jul 29, 2015 · 3 Suppose there are seven coins, all with the same weight, and a counterfeit coin that weights less than the others. Dec 5, 2021 · That is because if you follow a valid strategy assuming that A means "left heavier" and B means "right heavier", and in fact they are the other way around, you get exactly the same results as you would have done if your assumption was correct and the same coin was fake, but its weight differed in the opposite way. ans ) 2 iterations arrange 9 coins into 3 batches each of 3. what is the fewest number of weighings that you can make which will tell you which coin is the heavier one? Question: You have n coins | they all look identical, and all have the same weight except one, which is heavier than all the rest. Either way, you can narrow the light coin to being in one of the three piles. The counterfeit coin can be distinguished by weight - it is heavier than the rest. Each group will consinst $1$ ball. $2$ of the scales work, but the $3$ rd is broken and gives random results (it is sometimes right and sometimes wrong). ). 1 gram. ii) weigh 9/10, if they are different then the one that goes the same direction as 9/10 before is that direction. Suppose further that you have one balance scale and are allowed only two weighings. (10 points) Counterfeit Coins (a) Suppose you have 9 gold coins that look identical, but you also know one (and only one) of them is counterfeit. Bonus puzzle. How many weighings are necessary using a balance scale to determine which of the eight coins is the counterfeit one? Give an algorithm for finding this counterfeit coin. - QUESTION 1 Partition the coins into 3 gatherings of 3. A coin can weigh 9, 10 or 11 grams. The counterfeit coin is lighter than the others. The balance machine can't tell you the exact weight. One of the coins is heavier than the other 8. You are asked to identify the heavier coin with minimum number of weighingas possible. the coins are all the same except that one coin is counterfeit and does not have the same weight as the real coins. If there are 9 seemingly identical gold coins, eight real and one fake. Jan 31, 2015 · The pans are balanced: the 8 balls you just weighed all have the correct weight. Jul 21, 2014 · Number the coins 1 through 12. How do you find the fake gold coin? SOLUTION 5. If they are the same, then the one we didn't choose is the heavier, if one is heavier, that is the heavier ball. EDIT: Solution for five weighings: Label your coins 1 through 8. How can you find the one counterfeit coin, which is just slightly heavier than the rest? There are numerous ways to determine the counterfeit coin with two weightings, but the most straightforward approach is as follows: You are given n coins — they all look identical, and all have the same weight except one, which is heavier than all the rest. You have a balance. ) **(Note: When we compare 1,4 to 2,5, You have nine coins, of which eight are identical but one is lighter than the others (you don't know which one this lighter coin is). How does the "8 Coin Riddle" work? The "8 Coin Riddle" can be solved by dividing the 8 coins into 3 groups of 3, 3, and 2 coins. I can only use the balance beam 2 times to find the heavier coin. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. One of the coins is counterfeit and weighs slightly less than the other 8. You do not know which scale is broken. You have a balance scale that you may use only twice. The third weighing is 9v10. You have a pan balance with no weights. com Find step-by-step solutions and your answer to the following textbook question: You have eight coins. So the amount of extra weight will be the same as the stack number. If both sides equal 3, remove all six and weigh the remaining two. Time to solve is 30 minutes. n = 9 {8, 7, 5, 4, 3, 2, 1, 0, -10} (this isn't a downhill weighing) 40 Some Other Coinpelling Cases (Cointinued) Arithmetic progression weighings are when the multiplicities in a balanced weighing form an You are given N coins which look identical (assume N = 2^k). Select two groups of three coins each from the given coins and put them on the opposite cups of the scale. ) (Note: 9 can't be the same weight as 1 because we know that 9 is the counterfeit. The task is to find the minimum amount required to acquire all the N coins for a given value of K. Otherwise, it is the one indicated as lighter by the balance. 7) A woman ran into an old friend at the movies. Each real gold coin weighs exactly 1 gram, while each fake coin weighs exactly 1. If they are the same then 11 is the direction it went. You can either take two or three coins from which you can find the counterfeit one. In this case you fail if it balances. Case 2: Side of coin B goes down → Coin B is heavier. One of them is defective and weighs heavy than the others. First of all we will give a number to each ball Answer to Solved You have n coins | they all look identical, and all | Chegg. 8 coins, 7 are real and 1 is fake. Again, we have three possibilities. If you had more than penny, you must have at least pennies to leave a multiple of for the nickels, dimes, and quarters. You also have an unlimited supply of known real coins. Solution :-. All the coins are identical. May 21, 2013 · The "8 Coin Riddle" is a mathematical puzzle that involves determining the weight of a fake coin among 8 identical coins using only 2 weighings on a balance scale. Therefore, we can get the stack with only a single balance. You are handed 12 identical looking coins (numbered 1 through 12) and a balance scale and are told that one of the coins is counterfeit. So, you'd need a third bag to find out which bag is the outlier. Since $82 > 3^4$, you cannot determine which is the fake coin in only four more weighings. One of the coins is counterfeit and weighs less than the other coins. Feb 28, 2022 · You are given a list of N coins of different denominations. You have a digital scale (that tells the exact weight). If equal, 11 is counterfeit. A gold coin weigh 10 grams and a silver coin weigh a gram less. Compare the weight of two of those groups. 7. 4. 2018 Sep 13, 2015 · You have 12 coins and a balance scale, one of which is fake. 43. Initially, each coin is in its own separate group. Question: 1. how can one determine, in 3 weighings on a balance scale, which of the coins is counterfeit and Dec 10, 2021 · You have nine identical-looking coins. Question: You are given 9 identical looking coins. Sep 29, 2023 · After some number of uses of the scale, we can partition the coins into several groups, where it is known that any two coins in the same group have the same weight. Dec 19, 2006 · You have nine identical-looking stones. three weighings b. Mar 19, 2009 · Interview question for Software Engineering Manager. For example, if you are a 5'10" male estimating your ideal weight with the Devine formula, you would add (2. Jun 28, 2019 · A coin weighing problem is a problem that looks something like this: You have twelve coins. To find the lighter one we can compare any two coins, leaving the third out. com Consider the following problem: Suppose we have nine identical-looking coins numbered 1 through 9 and only one of the coins is heavier than the others. Eight of these coins are identical, but one is counterfeit. All real coins have the same weight. In this case, you know that the different marble is 9, 10, or 11, and that that marble is heavy. Nine of the stacks contain all real gold coins, and one of the stacks is made up entirely of fake gold coins. 1 gram or have an extra 0. Given a regular measurement scale, how would you determine in one weighing which bag does not have the gold coins? Nov 29, 2023 · There are 5 bags with 100 coins in each bag. You're given $3$ double-pan balance scales. What is the minimum number of weighings needed t Feb 18, 2018 · Find an answer to your question You have 8 coins which are all the same weight, except for one which is slightly heavier than the others (you don't know which c… kotharinikki4936 kotharinikki4936 18. What is the Counterfeit Coin Problem? The Counterfeit Coin Problem is a puzzle that tests your brainpower. Find the Fake Coin. VIDEO ANSWER: There is a set of nine coins and there is a counterfeit which is heavier than others. The You have reason to believe that one of the coins is a fake and has a different weight than the others, which all have the same weight. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. You may only use the balance scale two times. Step 1: you narrow down to group of coins. "Well," she says, "I need to know that you're really wise. Suppose we have nine identical-looking coins numbered 1 through 9 and only one of the coins is heavier than the others. Interview question for Software Engineer. Suppose we divide the coins into three piles, where at least two of them contain the same number of coins. Mar 9, 2015 · $\begingroup$ If you tweak I. Method: Divide the 100 coins into 2 groups A and B, each comprises 49 coins. The genuine coins all have the same weight. two weighings Dec 7, 2007 · You have 8 balls all look identical (in shape, color etc. Either way at the end of the first weighing you have at least 4 balls of the correct weight. Determine you strategy. Your mission is to pick out this one counterfeit coin by using the least amount Jan 15, 2018 · You have 9 coins. Question: There are nine identical- looking coins. May 18, 2023 · at least 3 and at most 9 weighings to determine which bag is fake. All balls look alike. CASE OF THE COUNTERFEIT COINS Now, if you have been able to solve the four problems Question: 1. (14p) There are 9 identical-looking coins, only one of which is fake coin lighter than the others and all real coins weigh the same. You also have a standard two-pan beam balance which allows you to place any number of items in each of the pans. It may be heavier or lighter - you do not know which. There are 13 coins whose appearances are identical. Dec 4, 2013 · Here the base-case would be to find the maximum number of coins from which you can find the counterfeit coins in just one-weighing. 2. You have four coins and can't find the odd one in one weighing, because there are three places for coins (two pans and off the balance), so there will be two unknown coins in the same place. You would need at most 9. a. Aug 12, 2022 · This is my favorite weight puzzle which have been asked from me in many interviews over the past few years. All of the coins in oneof these stacks are counterfeit, and all the coins in the other stacks aregenuine. Your heavy coins all have the same weight; same for the light coins. May 31, 2020 · You have a weighing scale with no measurements so you can just compare weight of balls against each other. What is the minimum number of weighings required to guarantee finding the Jan 14, 2020 · Interview question for Research Associate. One of the nine is counterfeit. All you are given is a set of BALANCE scales, which can compare the weight of any two sets of coins out of the total set of 24 coins. If you weigh 2, and they're different, you still wouldn't know which of the two is fake. = 11*K + 550 – 10*K = K + 550. design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. The counterfeit coin is known to be slightly lighter than the others. Apr 15, 2006 · You are given 12 coins that appear to be identical. Solution: Step 1: Divide the balls into three categories (C1, C2 and C3). Given a measurement scale, how would you find the heavy bottle? You can use the scale only once. Therefore by observing the extra weight in our picked coins, we can figure out the forged bag. Brain teaser: You have nine coins that are identical in weight except for one which is lighter than the others. They all look identical, but one is a fake and is slightly lighter than the others. You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. Case 1: Side of Coin A goes down → Coin A is heavier. +10) = 55 grams. . Each bag contains 100 coins. You have eight coins. Step 2: you narrow down to group of coins. You are alsogiven a balance scale. 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. Oct 7, 2020 · You have ten stacks of identical looking gold coins. Your goal is to (within 3 weighings) determine, with certainty, with is the defective coin. If equal, weigh 9,10,11 v 1,2,3 (not counterfeit). If the 3 coins balance, then the odd coin is among the remaining population of 2 coins. Case 3: Both sides are at same level → Coin C is heavier. What is the minimum number of weighings required to guarantee finding the Aug 22, 2020 · There are $14$ suspect coins, $13$ of which are good and have the same weight, and the last one is bad and have a different weight (heavier or lighter). 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. Suppose we have a balance and nine coins. Exampl Question: There are ten identical coins all the same weight except for one which is either heavier or lighter than the rest. 05. 23 coins are the same weight, but 1 coin is either heavier or lighter. 9. You ave given 9 identical looking gold coins numbered 1 through 9 and one balance scale. How do you do it? Solution. You can use a balance scale to compare weights in order to find which is the defective ball. So far, with $1$ weighing, we have $3$ balls left. You can do this in 3 weighings:Start by placing 4 coins on each side of the balance. If equal, 12 is the counterfeit and weigh it against any other coin to determine if it’s heavy or light. Using a balance scale only twice, find the counterfeit coin. You also have a simple weighing balance which can compare weights: In exactly two weighings, how can you determine the lighter coin? Question: problem2(counterfeit coins) (a) Suppose you have 9 gold coins that look identical, but you also know one (and only one) of them is counterfeit. Now put the 2 groups of 3 coins on the scale. How many minimum number of measurements are needed to find the heavy coin? 2. Thus the problem is solvable in two weighings. If the first two coins had the same weight and the first and third had distinct weights, then the third coin needs to have a different weight. By splitting up to 3 groups each step, after each step you should be able to narrow down your suspected coin by 3 times. If you weigh 9, and they're all the same, you know that the 10th is the fake. The coins look alike, but one of them is a counterfeit. In one bag the coins are silver, in the others gold. For your second weighing, you have to use piles of size 1, which will tell you which is light (if the coins weighed are equal, the third is light, and if they're unbalanced, the lighter is the light coin). A IQ question: I have 9 coins and 8 have the same weight and the last one is heavier. Let us assume that, 9 identical coins are denoted as 1, 2, 3, 4, 5, 6, 7, 8 and x . Using the scale only twice, figure out a way to find the counterfeit coin. How can you find the counterfeit coin? Sep 23, 2020 · question. Jan 11, 2017 · 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. You are allowed only two weightings. What is the number of weighing required to separate the gold from fake coins? (all gold coins have equal weights & all fake coins too have the same weight) Jul 22, 2024 · Puzzle: Given 10 identical bottles of identical pills (each bottle contains 100 pills). You have n coins | they all look identical, and all have the same weight except one, which is heavier than all the rest. If the first two coins had a distinct weight with the first and third coin having the same weight, then the You have reason to believe that one of the coins is a fake and has a different weight than the others, which all have the same weight. You are given one beam balance with two pans. two weighings. Draw a decision tree for using a balance scale to determine the counterfeit coin and whether it is heavier or lighter in the minimum number of weighings. By this example, I introduce some notation: Case 1a) Three coins and the counterfeit is H(eavier) (equivalently, one can assume otherwise and proceed in the similar lines). Besides, it doesn't tell the results to you right away and only prints the results after you have weighed twice. How can you identify the lighter coin in the least amount of weighings?. Oct 16, 2023 · b. 6) There's no bribing the guards or any other trick. You are only told that the fake weighs di fferently than the others (so you don't know if it is lighter or heavier than the real coins). Sep 11, 2021 · You have 9 identical coins of which 8 have the same weight - 46793341 If all their weights are the same, then the fourth coin needs to have a different weight. (15 points) Suppose we have nine identical looking coins numbered 1 through 9. Consider the following problem: (a) Suppose we have nine identical-looking coins numbered 1 through 9 and only one of the coins is heavier than the others. Jan 18, 2023 · Puzzle: You are provided with 8 identical balls and a measuring instrument. 2 piles of size 4: If you weigh these Mar 27, 2020 · you have n> 2 identical-looking coins and a two-pan balance scale with no weights. So for our second one possibility is to weigh 9,10,11 against 1,2,3 (1) They balance, in which case you know 12 is the different marble, and you just weigh it against any other to determine whether it is heavy or light. I have 9 coins, out of which 8 coins are identical in weight and one is lighter in weight. A pair of coins is selected at random without replacement from the coins. This is because. 3) Test 2a, Test 3 of the coins from the group of 5 coins against any 3 coins from the population of 8 coins: a. You also have a balance scale, on which you can place one set of coins on one side, and another set of coins on the other, and the scale will tell you whether the two sets have the same weight, and if Jan 18, 2023 · 11*K + (55 – K)*10 [because we have picked K coins from K th stack]. However, one of the coins is counterfeit, and the weight of this coin is slightly different than that of the other 11. Whenever you weigh two coins from different groups, there are two possibilities. Question: You have n coins | they all look identical, and all have the same weight except one, which is heavier than all the rest. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. Design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. If this is impossible, explain why. It's not quite clear why the problem has been set up for 8 and not 9 coins. You have 10 stacks of 10 gold coins. If they weigh the same, the fake is among the remaining two coins, and weighing these two coins will identify the lighter fake. I also have a balance beam to weigh the coins with. if the balance shows no movement then the 3rd batch is under You have 9 gold coins. This scale lets you put any number of these coins on either side and will determine which side is heavier or if the sides are equal. Although similar problems distinct objects into distinct bins and identical objects into distinct bins have closed-form solutions, the "identical objects into identical bins" problem presents some There are 10 identical bags of coins. What is the minimum number of weighings needed to determine which stack is fake? Question: You have n coins | they all look identical, and all have the same weight except one, which is heavier than all the rest. How to check the same if there are 11 stacks of 10 coins? We can continue the same process as the optimal one. For the second weighing one side of the pan should have 3 balls of the correct weight. it is lighter than a real coin. Identical objects into identical bins is a type of problem in combinatorics in which the goal is to count the number of ways a number of identical objects can be placed into identical bins. " Question 6. Apr 22, 2015 · I know I need at least 2 weighings to find the heavier ball since 3^2 = 9. If not equal, the direction of 9,10,11 will determine heavy or light. Puzzle. Using only a two-pan balance, … read more There are 9 coins, all except one are the same weight, the odd one is heavier than the rest. 2018 Sep 2, 2016 · Unless you have any extra information about the input, ⌈log_3_(N)⌉ is the best you can reach. Scenario #1: Both groups weigh the same. How many weighings are necessary to identify both the heavier and lighter coin? I can do it in five, but I strongly suspect you can do it in fewer. 5) You may write things on the coins with your marker, and this will not change their weight. Since you have one coin of each type, cents are already determined, leaving you with a total of cents remaining for coins. This is the solution. How many measurements do you need so that you will be… The correct option is C 2 Let's try to solve this in simple steps: Step 1: Segregate all 9 balls in three sets of 3. The counterfeit coin is either heavier or lighter, but you don't know which in advance. Split the coins into 3 groups – 2 groups with 3 coins each and 1 group with 2 coins. You must determine which is the odd one out using an old fashioned balance. You must have more penny. There are 9 coins, all except one are the same weight, the odd one is heavier than the rest. Bonnie N. … Answer to Solved You have n coins | they all look identical, and all | Chegg. The only scale available is a balance scale, on which you can weigh any number of coins against each other. Say (1, 2, 3) , (4, 5, 6) and (7, 8, x) . But you only have more coins to assign. Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of the weight of 1. Divide the 9 balls into 3 groups of 3. So, the base-case for this approach would be dividing the available coins by taking three at a We would like to show you a description here but the site won’t allow us. With proper strategy, at most, how many weighings are required to identify the counterfeit coin? Jul 16, 2015 · The maximum number possible is three. You have only 3 chances to weigh the balls in any combination using the scales. Jun 10, 2023 · You have given nine identical-looking gold coins numbered 1 through 9 and one balance scale. There is a balance scale with a weighing pan on each side. Let’s compare the weight of X against the weight of Y: Sub-scenario 2a: X and Y have Mar 22, 2010 · You have 24 coins. Case 1) :- Taking any two pairs and weighing them . Then, we compare the weight of the top coins (#0 #1 #2) vs the bottom coins (#6 #7 #8) so we know whether the heaviest coin is in the top, middle, or bottom. you also have a pan balance. A real coin weighs 10 grammes. You may use the balance twice. Is it possible to find the light weight coin with only two weighings, using pan balance?. You have an analytical scale that can determine the exact weight ofany number of coins. I was thinking make two groups from the 8 -> two groups of 4 which is in itself contains another subset = { (1)a (3)a } and { (1)b (3)b }. A precious jewel is embedded in one of the stones. You have a scale - balance type with 2 trays - but can only load it twice. You also have a balance scale, on which you can place one set of coins on one side, and another set of coins on the other, and the scale will tell you whether the two sets have the same weight, and if not, which is the heavier set. You also have a balance scale, on which you can place one set of coins on one side, and another set of coins on the other, and the scale will tell you whether the two sets have the same weight, and if not, which is You have reason to believe that one of the coins is a fake and has a different weight than the others, which all have the same weight. 3 × 10) kg to 50 kg to get 73 kg, or ~161 lbs. Question: You have n > 2 identical-looking coins and a two-pan balance scale with no weights. asked • 08/23/16 There are 8 identical looking coins, one of these coins is counterfeit and known to be lighter than the others. So how do we solve this specific case? Sep 2, 2022 · You've $8$ identical-looking coins. 4) Suppose you have 9 coins, all identical in appearance and weight except for one that we know is heavier than the other 8 coins. Weight the Oct 20, 2012 · I will start with a simple case of three coins and describe the method. Is it possible to detect the counterfeit coin in at most two weighings with a two-pan scale? If so, describe an algorithm and explain why it works. Apr 1, 2022 · Y contains 3 coins from C and the remaining 1 from B; Observe three coins from A are not used in X or Y. In addition, once you have paid for a coin, we can choose at most K more coins and can acquire those for free. And. Eight of the stones weigh the same, but the stone containing the jewel weighs slightly more than the others (not enough of a difference to tell without a scale). Nov 17, 2015 · If one of them is heavier, then that group has the heavier. After weighing the equal-sized piles, we can eliminate ~2/3 of the coins! After weighing the equal-sized piles, we can eliminate ~2/3 of the coins! We would like to show you a description here but the site won’t allow us. One of the coins is heavier than the other 8 . three weighings. Now, imagine the nine coins in three stacks of three coins each. The weight balance compares the weight of two sides on the balance instead of giving numerical measurement of weights. All the coins weigh the same but $1$ coin is lighter than the rest. Can you find all possible ways to solve the puzzle? No time limit for this one and no Answer / sabarish. So, maximum(two, three) = three. . What is the minimum number of ratings that always identify a counterfeit one? There are nine coins, so that's right. There are 9 coins before you. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. 1 coin is left off the balance. If one is heavier you can only focus on that. Hope you can understand the logic behind it. Describe a method for fi nding the fake coin using only a pan balance and the coins themselves that takes as few weighings as possible. Take coin A and coin B and put them on the weighing scale. (a) Show that two weighings suffice to determine which of the nine coins is the counterfeit one. Develop a method for finding the heavier counterfeit coin given these constraints. first weigh : weigh 2 batches and find the defective. To show that it cannot be done in two, consider AB vs DE. 3. " She takes out nine identical coins (of course, all of them have her face on them- she is the queen, after all!). 02. Mar 1, 2021 · You have 9 balls, 8 of which have the same weight. Solution: All of the formulas have the same format of a base weight given a height of 5 feet with a set weight increment added per inch over the height of 5 feet. Oct 17, 2020 · Find the fake ball in 3 weighs—9 balls 1 different weight puzzle. So here is a challenge. Apr 3, 2024 · Given 8 identical coins out of which one coin is heavy and a pan balance. You have 9 balls identical in size and appearance. "One of these is counterfeit and weighs more than the others. You have nine identical looking coins. Explain how you can use a balance scale to determine which coin is the fake in exactly a. There are 3 outcomes:*The balance is horizontal (both sides weigh equally) -> the fake coin is the one not on . A counterfeit coin weighs 11 grammes. Recursively apply the same algorithm to the lightest group. (1, 2, 3) and (4, 5 ,6) = They are equal . Eight of the coins have the same weight, while the ninth is counterfeit and weighs less than the others. All the real coins weigh the same, but the fake coin weighs less than the rest. How many times do you needd to use the scale to determine which type of coin each bag contains ? @Camden No luck is needed. Each bag contains coins of equal weight, but we do not know what type of coins a bag contains. May 9, 2018 · Find an answer to your question You have nine identical coins, of which 8 have the same weight and one has a different weight. Take any six coins of the eight coins, put 3 on the left side and three on the right side. Divide 9 coins into pair of 3 . Question: Twelve Coins – You have 12 identical-looking coins, one of which is counterfeit. You have a modern scale that provides an accurate readout. How can we find the fake coin in two weighings? (2) (5p) Now, suppose there are 8 apparently identical-looking coins. Develop a divide-and-conquer method for finding the heavier counterfeit coin given these constraints. b) if you have coins then you can apply the same approach and find the fake coin with just n steps. So you can only weight coins themselves in two sides of the scale todetermine heavier side. In at most 3 weighings, give a strategy that detects the fake coin. Luckily, the balance scale can reveal the counterfeit coin because its weight is slightly different than the weight of the other coins. what… vinayak4807 vinayak4807 09. Make the same tactic again: Make $3$ groups. All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. Determine which ball is the odd one and if it’s heavier or lighter than the rest. Now you have cents remaining for 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. Every genuine coin weighs 10 grams, and every fake weighs 11grams. Question: There are 10 stacks of 10 identical-looking coins. 1 grams. Using a balancing scale, devise a strategy to identify the counterfeit in a total of TWO weighings. Exactly one of the coins is counterfeit and heavier than the others. Two counterfeit coins of equal weight are mixed with identical genuine coins. we do not now if the counterfeit coin is heavier or lighter than the real coins. You can use a two sided balance system (not the electronic one). 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. A second pair is selected at random without replacement from the remaining coins. We would like to show you a description here but the site won’t allow us. This fake coin is a tiny bit heavier or lighter than the rest, but you don’t know which. If the two coins tested weigh the same, then the lighter coin must be one of those not on the balance. Fake coin weighs more. First weighing: 1,2,3,4 v 5,6,7,8. You can pay an amount equivalent to any 1 coin and can acquire that coin. You need to figure out which it is. The difference is perceptible by weighing them on a scale, and only the coins themselves may be weighed. There is also a simple balance scale to be used for weighing and determining the incongruent coin. You want to find which suspect coin is bad, and as much as possible (see below), whether it is heavier or lighter. All the coins visually appear the same, and the difference in weight is imperceptible to your senses. Eleven of them weigh the same; one of them is either heavier or lighter than the other eleven. Say group a is heavier. Weigh 9/10 against 11/4. The only scale available is a balance scale. If the first weighing does not yield a balance, the lighter fake is among the three lighter coins. Three groups of equal number of coins, weigh two of them against each other, and you'll see which of the three groups has the lower weight. Picture this: you have several coins that look exactly the same, but one of them is not real—it’s a counterfeit. Step 3: you narrow down to group of #6 #7 #8 First, we compare the weight of the left coins (#0 #3 #6) vs the right coins (#2 #5 #8) so we know whether the heaviest coin is in the left, middle, or right. Jun 6, 2024 · suppose that we have 12 coins that look identical. You want to figure out which one is the counterfeit, and whether it is heavier or lighter. Suppose further that you have a balance scale and are allowed only two weightings. The pans are unbalanced: The 4 balls you did not weigh all have the correct weight. Sep 5, 2023 · You have 8 coins which are all the same weight, except for one which is slightly heavier than the others (you don't know which coin is heavier). b. 65. You come to her offering your services. If there is only 1 bag with forgeries, then take 1 coin from the first bag, 2 coins from the second bag . How do you find the heavier coin?. The Question: You have n coins | they all look identical, and all have the same weight except one, which is heavier than all the rest. You are only allowed 3 weighings on a two-pan balance and must also determine if the counterfeit coin is heavy or light. The odd coin is among the population of 8 coins, proceed in the same way as in the 12 coins problem. (2) 9,10,11 is heavy. Question: Lighter or heavier? You have n > 2 identical-looking coins and a two-pan balance scale with no weights. 6) You have nine coins in your possession. Then it is impossible to determine the different coin and whether it is lighter or heavier than the others by using a pan balance 3 times. Question: You have eight coins and a balance scale. Give it a try before going ahead. You weigh the two groups. The counterfeit coin weighs slightly less than the others. All of the coins in one of these stacks are counterfeit, all the other coins are not. All of them have same weight except one defective ball which is heavier than others. You have a weighing scale with no measurements so you can just compare weight of balls against each other. Mar 3, 2023 · Now we know that the real coins all weigh 1 gram while the forged coins weigh 1. Find the fake ball among 9 balls in 3 weighs. Besides, we have three apparently identical balances (the kind that dðesn't tell the exact weight), and one balance is broken whose outcomes are unrelated to the actual situations. you also have an oldâ€style balance, which allows you to weigh two piles of coins to see which one is heavier (or if they are of equal weight). 1 gram of weight. The two counterfeit coins have the same combined weight as two normal coins. Among these coins one coin is other lighter or heavier than the others, which have the same weight. Say the weight of the collective coins comes as 55. In order to protect your reputation as local philanthropist you need to find the fake coin so the rest can be donated to the new museum. We will give the Real coins a weight value of 1 and the fake a weight value of 2. Nov 16, 2015 · Now you have shown that three are sufficient. If both are equal in weight then the third set has the heavier ball. 5 grams. where x is lighter in weight from others . The counterfeit coin is lighter than the rest; the other 11 coins weigh the same amount. Now weigh any two sets against each other. The remaining one is defective and heavier than the rest. vhayo jgkdo nrrzuj wkgx dsppd jhnci oqi bkrsesk hvdo wixojbz