You have nine identical coins of which 8 have the same weight. Jul 16, 2015 · The maximum number possible is three.

You have nine identical coins of which 8 have the same weight. 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. First of all we will give a number to each ball Jan 15, 2018 · You have 9 coins. The counterfeit coin weighs slightly less than the others. Splitting 9 coins into three groups and thinking of each as a "big coin", reduces the problem to the previous one: it takes just one weighing to detect the lighter group. To show that it cannot be done in two, consider AB vs DE. How do you find the heavier coin?. If not equal, the direction of 9,10,11 will determine heavy or light. Astute readers will recognize that this is the base 3 (or ternary) number system. 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. You weigh the two groups. Step 2: Place two of the three groups on either side of the balance. 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. what… vinayak4807 vinayak4807 09. Suppose we have a balance and nine coins. All real coins weigh the same. Develop a method for finding the heavier counterfeit coin given these constraints. Jan 31, 2015 · The pans are balanced: the 8 balls you just weighed all have the correct weight. 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+ . Step 2: you narrow down to group of coins. You have a weighing scale with no measurements so you can just compare weight of balls against each other. First weighing: 1,2,3,4 v 5,6,7,8. Recursively apply the same algorithm to the lightest group. You are alsogiven a balance scale. The two counterfeit coins have the same combined weight as two normal coins. Divide the 9 balls into 3 groups of 3. All the real coins weigh the same, but the fake coin weighs less than the rest. 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 }. However, in the counterfeit bag, all coins weigh either 9 or 11 grams. Compare the weight of two of those groups. The above solution shows that 1 weighing is sufficient to detect a lighter fake among 3 coins. If equal, weigh 9,10,11 v 1,2,3 (not counterfeit). 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. A second pair is selected at random without replacement from the remaining coins. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. . 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. Click here👆to get an answer to your question ️ 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). Question: Twelve Coins – You have 12 identical-looking coins, one of which is counterfeit. How do you find the fake gold coin? You have nine identical looking coins. 6) There's no bribing the guards or any other trick. 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). You are only allowed 3 weighings on a two-pan balance and must also determine if the counterfeit coin is heavy or light. You have a pan balance with no weights. Exampl Jan 18, 2023 · You have 20 white and 13 black balls in a bag. 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. 4,5,6 same 1,2,3 is lighter 4,5,6 is lighter (Similar to previous All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. If equal, 12 is the counterfeit and weigh it against any other coin to determine if it’s heavy or light. Case 1: Side of Coin A goes down → Coin A is heavier. I also have a balance beam to weigh the coins with. 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. Find the fake ball among 9 balls in 3 weighs. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. Jul 29, 2022 · You can translate the two digits of the license plate to the coins as follows: 01 is coin 1, 02 is coin 2, 10 is coin 3, 11 is coin 4, 12 is coin 5, 20 is coin 6, 21 is coin 7 and 22 is coin 8. A well-known example has up to nine items, say coins (or balls), that are identical in weight except one, which is lighter than the others—a counterfeit (an oddball). Give it a try before going ahead. 2. 05. One of the nine is counterfeit. You pull out 2 balls one after another. Let us assume that, 9 identical coins are denoted as 1, 2, 3, 4, 5, 6, 7, 8 and x . EDIT: Solution for five weighings: Label your coins 1 through 8. Sep 13, 2015 · You have 12 coins and a balance scale, one of which is fake. 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. They all look identical, but one is a fake and is slightly lighter than the others. Jul 16, 2015 · The maximum number possible is three. By splitting up to 3 groups each step, after each step you should be able to narrow down your suspected coin by 3 times. Step 1: you narrow down to group of coins. The genuine coins all have the same weight. With proper strategy, at most, how many weighings are required to identify the counterfeit coin? Sep 23, 2020 · Solution :-. - QUESTION 1 Partition the coins into 3 gatherings of 3. So the amount of extra weight will be the same as the stack number. 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. Bonus puzzle. The only scale available is a balance scale, on which you can weigh any number of coins against each other. Divide 9 coins into pair of 3 . Feb 28, 2022 · You are given a list of N coins of different denominations. Your heavy coins all have the same weight; same for the light coins. Case 2: Side of coin B goes down → Coin B is heavier. Dec 31, 2018 · Let’s name those remaining coins as A, B, C. A pair of coins is selected at random without replacement from the coins. We would like to show you a description here but the site won’t allow us. You need to identify the counterfeit bag in just one weighing, and you have a digital scale that provides accurate weights. The Nov 13, 2023 · You have 12 coins and a balance scale, one of which is fake. Method: Divide the 100 coins into 2 groups A and B, each comprises 49 coins. Oct 7, 2020 · You have ten stacks of identical looking gold coins. Since $82 > 3^4$, you cannot determine which is the fake coin in only four more weighings. If the balls are of same color, then you replace them with a white ball – but if they are of different color, you replace them with a black ball. There is a balance scale with a weighing pan on each side. 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 can pay an amount equivalent to any 1 coin and can acquire that coin. You have a scale - balance type with 2 trays - but can only load it twice. Puzzle. The pans are unbalanced: The 4 balls you did not weigh all have the correct weight. You have only 3 chances to weigh the balls in any combination using the scales. One of the coins is counterfeit and weighs slightly less than the other 8. Time to solve is 30 minutes. 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. Step 3: you narrow down to group of Lighter or heavier? You have n > 2 identical-looking coins and a two-pan balance scale with no weights. (a) Show that two weighings suffice to determine which of the nine coins is the counterfeit one. Using the scale only twice, figure out a way to find the counterfeit coin. The lighter coin is in third pair . Explain how this can be done. Suppose further that you have one balance scale and are allowed only two weighings. Jan 18, 2023 · 11*K + (55 – K)*10 [because we have picked K coins from K th stack]. where x is lighter in weight from others . Step 3: Take two coins from the third group and place one on each side of the balance. 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 If there is only 1 bag with forgeries, then take 1 coin from the first bag, 2 coins from the second bag . Can you find all possible ways to solve the puzzle? No time limit for this one and no Apr 13, 2024 · You have 10 bags of 100 coins, and in all of them except for one, every coin weighs exactly 10 grams. Case 1) :- Taking any two pairs and weighing them . You want to find which suspect coin is bad, and as much as possible (see below), whether it is heavier or lighter. Feb 12, 2020 · b) if you have coins then you can apply the same approach and find the fake coin with just n steps. You have 9 balls identical in size and appearance. Eight of the coins have the same weight, while the ninth is counterfeit and weighs less than the others. The third weighing is 9v10. Aug 12, 2022 · This is my favorite weight puzzle which have been asked from me in many interviews over the past few years. 1 grams. 2018 Nov 16, 2015 · Now you have shown that three are sufficient. Besides, it doesn't tell the results to you right away and only prints the results after you have weighed twice. In this case you fail if it balances. Mar 19, 2009 · Interview question for Software Engineering Manager. The balance machine can't tell you the exact weight. It may be heavier or lighter - you do not know which. Problem: Find the counterfeit and whether it is lighter or heavier, using a balance just three times. May 31, 2020 · You have a weighing scale with no measurements so you can just compare weight of balls against each other. Therefore, we can get the stack with only a single balance. One of the coins is heavier than the other 8. You ave given 9 identical looking gold coins numbered 1 through 9 and one balance scale. Say group a is heavier. In addition, once you have paid for a coin, we can choose at most K more coins and can acquire those for free. If equal, 11 is counterfeit. three weighings b. The counterfeit coin can be distinguished by weight - it is heavier than the rest. Step 1: Divide the 9 coins into three groups of three coins each. Nine of the stacks contain all real gold coins, and one of the stacks is made up entirely of fake gold coins. 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. Apr 22, 2015 · I know I need at least 2 weighings to find the heavier ball since 3^2 = 9. How can we find the fake coin in two weighings? (2) (5p) Now, suppose there are 8 apparently identical-looking coins. 9 coins; one coin is counterfeit. You are asked to identify the heavier coin with minimum number of weighingas possible. Now, imagine the nine coins in three stacks of three coins each. Question: Suppose you have eight coins, one of which is counterfeit (either heavier or lighter than the other seven). Determine which ball is the odd one and if it’s heavier or lighter than the rest. two weighings. To find the lighter one we can compare any two coins, leaving the third out. In addition, you have a $15$ th coin that is known to be good. Mar 27, 2020 · you have n> 2 identical-looking coins and a two-pan balance scale with no weights. It's not quite clear why the problem has been set up for 8 and not 9 coins. So you can only weight coins themselves in two sides of the scale todetermine heavier side. There are 9 coins, all except one are the same weight, the odd one is heavier than the rest. You also have a simple weighing balance which can compare weights: In exactly two weighings, how can you determine the lighter coin? 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. Once you take out the balls, you do not put them back in the bag – so the balls keep reducing. The task is to find the minimum amount required to acquire all the N coins for a given value of K. You may use the balance twice. Suppose we have nine identical-looking coins numbered 1 through 9 and only one of the coins is heavier than the others. If the two coins tested weigh the same, then the lighter coin must be one of those not on the balance. In at most 3 weighings, give a strategy that detects the fake coin. All balls look alike. = 11*K + 550 – 10*K = K + 550. Aug 23, 2016 · If you can put as many of the coins as you want on either side of the balance, you could determine the light coin in 3 weighings. +10) = 55 grams. If one is heavier you can only focus on that. 65. For the second weighing one side of the pan should have 3 balls of the correct weight. One of them is defective and weighs heavy than the others. One of the coins is counterfeit and weighs less than the other 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. You must determine which is the odd one out using an old fashioned balance. Oct 17, 2020 · Find the fake ball in 3 weighs—9 balls 1 different weight puzzle. Sep 11, 2021 · You have 9 identical coins of which 8 have the same weight - 46793341 Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. Say (1, 2, 3) , (4, 5, 6) and (7, 8, x) . Determine you strategy. Two counterfeit coins of equal weight are mixed with identical genuine coins. (1, 2, 3) and (4, 5 ,6) = They are equal . Each real gold coin weighs exactly 1 gram, while each fake coin weighs exactly 1. The counterfeit weighs either less or more than a real coin. Using a balance scale only twice, find the counterfeit coin. The difference is perceptible only by weighing them on scale —but only the coins themselves can be weighed. you also have a pan balance. Explain how you can use a balance scale to determine which coin is the fake in exactly a. Find step-by-step solutions and your answer to the following textbook question: You have eight coins. All the coins visually appear the same, and the difference in weight is imperceptible to your senses. Scenario #1: Both groups weigh the same. a. design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. Split the coins into 3 groups – 2 groups with 3 coins each and 1 group with 2 coins. 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. What would be 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. How to check the same if there are 11 stacks of 10 coins? We can continue the same process as the optimal one. . #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. Take coin A and coin B and put them on the weighing scale. Start by splitting the coins four-and-four on either side, and see which side is lighter. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. If they are of equal weight, then the odd coin out is in the third group. 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. How do you do it? Solution. Question: 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. 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. 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. Question: 1. I can only use the balance beam 2 times to find the heavier coin. Design a (1) algorithm to determine whether the fake coin is lighter or heavier than the others. Jan 7, 2017 · 5) You may write things on the coins with your marker, and this will not change their weight. Jul 21, 2014 · Number the coins 1 through 12. 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. A IQ question: I have 9 coins and 8 have the same weight and the last one is heavier. So how do we solve this specific case? Dec 10, 2021 · You have nine identical-looking coins. Sep 2, 2016 · Unless you have any extra information about the input, ⌈log_3_(N)⌉ is the best you can reach. 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. Again, we have three possibilities. There are 9 coins before you. Case 3: Both sides are at same level → Coin C is heavier. If this is impossible, explain why. Weight the Question: You are given 9 identical looking coins. Jul 29, 2015 · 3 Suppose there are seven coins, all with the same weight, and a counterfeit coin that weights less than the others. The only scale available is a balance scale. In this case, you know that the different marble is 9, 10, or 11, and that that marble is heavy. The weight balance compares the weight of two sides on the balance instead of giving numerical measurement of weights. The counterfeit coin is lighter than the rest; the other 11 coins weigh the same amount. Either way at the end of the first weighing you have at least 4 balls of the correct weight. You have a balance. (2) 9,10,11 is heavy. Now put the 2 groups of 3 coins on the scale. Among the nine, eight coins are genuine and weigh the same whereas one is a fake, which weighs less than a genuine coin. 1 2 3 4 5 6 7 8 9 1,2,3 vs. Otherwise, it is the one indicated as lighter by the balance. You also have a standard two-pan beam balance which allows you to place any number of items in each of the pans. Question: There are nine identical- looking coins. jnek wbtso xypobuls zoku uvun cucnrjr imt wepvw eihdx twtuwjl