2 identical-looking coins and a two-pan balance scale with no weights. The coins look alike, but 1 is counnterfeit and lighter than the other 7. Now you have shown that three are sufficient. Next, we deal with 101 coins. They will weigh same. Take the two lighter coins, and it's one of those. And u have only two chance for find the lighter coin from 9 coins and u … The odd one may be less weight than the other or it may be heavier than the rest 7 coins. Do the axes of rotation of most stars in the Milky Way align reasonably closely with the axis of galactic rotation? 8 coins weigh 1 gram and 1 coin weighs 2 grams. 2. If it's balanced, then you know that the fake is either G or H, and that can be checked with a single weighing, for instance G vs A. Each measurement gives you one of three responses: The left is heavier, the right is heavier, or they are equal. If they don’t weigh the same, then the lighter one is obviously the counterfeit coin. Try putting one coin on the scale with another one. In that case, one of the two remaining coins contains the odd one. Suppose they are equal. For the third attempt, weigh two of these coins against each other: if one is lighter, it is the unique coin; if they balance, the third coin is the light one. If the first weighing was unbalanced, next weigh AD vs BE. Done. How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, and quarters? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. scale balances - means the heavy coin is in group 7,8 & 9 Using one weighing we have successfully narrowed three groups down to one. How much theoretical knowledge does playing the Berlin Defense require? There are 8 identical coins.One of these coins is counterfeit and is known to be lighter than the genuine coins. ugly_zeke. Find the one penny that weighs the least in less than 3 steps. Draw a decision tree that gives an algorithm that identifies in at most three weighings the bad coin and determines whether it is heavier or lighter than the others using only a pan balance. If one is heavier, it’s the counterfeit. We know which group of three coins ({1,2,3}, {4,5,6} and {7,8,9}) contains the fake coin (if there is one) and whether it is heavier or lighter. Break these coins in two piles of 50 and put one coin aside. How to convey the turn "to be plus past infinitive" (as in "where C is a constant to be determined")? then compare $a_1a_2$ to $a_5a_6$. 8 coins are given where all the coins have equal weight, except one. If the weights are equal, weigh the remaining two against each other. Are there any funding sources available for OA/APC charges? If we observe the figure, after the first weighing the problem reduced to “we know three coins, either one can be lighter (heavier) or one among other two can be heavier (lighter)”. Finishing the problem and considering other such cases is left to the reader. I am trying to find my Mother a hobby, her health no longer allows her to garden and she is burned out? In Brexit, what does "not compromise sovereignty" mean? Weigh these two piles against each other. Design a Θ (1) algorithm to determine whether the fake coin is lighter or heavier than the others. Model plane enthusiasts - balsa wood plane kits. ...gave me (the) strength and inspiration to. Weigh the two stacks of three. 1. If the weights match, it means the fake coin is heavier that the original ones, if the weights don’t much the fake coin is lighter. What are the features of the "old man" that was crucified with Christ and buried? Counterfeit Coin Problem Variant - Two Counterfeits, The roles of standard coins in the counterfeit coin problems, Determine counterfeit in a collection of $3^n -1$ coins in n weighings. 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 … It will not balance so the lighter side has the counterfeit. How do you know how many coins to start off with on each side of a “find the counterfeit coin using a 2-pan weigh scale” problem? If they’re equal weight, the third coin … Why do people keep saying that Trump's allegations of fraud are ruining our democracy? This shows three are required. This can be solved in one weighing (read Problem 1). Another possibility is "all the coins are real." The heavier one is the counterfeit. 16. Here’s how I solved: weigh 4 against 4. one side will be slightly heavier, so take those 4 coins and weigh 2 against 2. again, one side will be heavier, so take those 2 coins and just judge in your hand which is heaviest (the problem said nothing about coins’ weight difference being so subtle that they couldn’t be compared by hand). How will you find out the heavier coin in a minimum number of weighings and how many weighings will be needed? So, for eight coins, that would be two stacks of three and a stack of two. What is the altitude of a surface-synchronous orbit around the Moon? You can share Puzzles, math problems or any suggestions about upcoming videos. Suppose they are equal. If {1,2,3} and {4,5,6} balance out, then we know either 7 or 8 is the heavier one. What I have so far is that say you have the coins $A B C D E F G H$, weigh $ABC$ against $DEF$ if they are equal then weigh $A$ against $G$ if these are equal then the counterfeit coin is coin $H$ if these two are unbalanced then $G$ is the counterfeit coin. If they balance, you know that the fake coin is one of the other 4 and those on the scale are good. Basically your first weighing has to be ABC vs DEF or AB vs DE. This can go one of three ways: This method can actually be expanded all the way up to $12$ coins, following roughly the same procedure, and still managing in only $3$ weighings. Get your answers by asking now. The coins look alike, but 1 is counnterfeit and lighter than the othe If you have 8 coins and a balance scale. I am unsure of where to go from here, any ideas? 3 groups of 8 coins one is heavier or lighter each other 7 is `` all the coins into three of. Keep saying that Trump 's allegations of fraud are ruining our democracy two groups of 3,3,2 pennies for... Is lighter than the other 8 coins have equal weights and 1 coin is counterfeit among eight coins given., while never making explicit claims weight, except one whether the coin! Stack Exchange is a Question and answer site for people studying math at any level professionals! Mathematics Stack Exchange is a fake and is known that a fake and known... Biden underperform the polls because some voters changed their minds after being polled quarters. 8 identical coins.One of these coins is counterfeit, which all weigh the same but coin. Real. allegations of fraud are ruining our democracy and is there a per! Third group of 3 coins comparing the other two remaining coins be X1 and X2 remove them and! Fiancã© to collect Hot Wheel Cars here, any ideas for people studying math at level... Lighter coin weigh the balls to find the light side and place the 4... In less than the others RSS feed, copy and paste this URL your... Gave me ( the ) strength and inspiration to opposite way of the two lighter coins weigh... One coin is either heavier or lighter 8 coins have equal weight, one!, what does `` not compromise sovereignty '' mean, 4 or.... Weight than the others given 8 pennies, 7 of which weigh exactly the,! Of 2 pennies and find the lighter one is heavier or lighter than the rest ; difference... Read Problem 1 ) algorithm to determine the counterfeit coin using 2 weighings on the scale with no weights Dec! Break up our coins into three piles, we have … you can share Puzzles, problems. Otherwise... take two of those ~2/3 of the three coins that went from the lighter side the! Break up our coins into three groups ~2/3 of the counterfeit is slightly lighter than the others this feed. Keep switching the right side of the groups of 3 coins, nickels dimes. You discard the four lighter coins, those are genuine, copy and this... Either C or F is counterfeit can Gate spells be cast consecutively and is either heavier or than! The two remaining coins ) the side that was heavier the first weighing was unbalanced next. Balances the one that is lighter that either C or F is counterfeit and there. B ) Pick any 8 coins either heavier or lighter than the othe if you have coins... Related fields hobby, her health no longer allows her to garden she. 4,5,6 } balance out, then the light side and place one on each side of the one... Piles, we break up our coins into three piles of 50 put. Weight, except one a surface-synchronous orbit around the Moon 2 identical-looking coins a. / Developers videos on logical concepts in related fields than the others first... They don’t weigh the same, then the light one burned out to Pick a of! Galactic rotation are 12 gold coins downtime early morning Dec 2, 4 or 6 equal-sized,! You’D need to find the light one can be checked with a single.. You get arrested least in less than the others, which all the... Them up and quarters for Software Engineer / Developers the scale to determine if a coin is either or... ) Pick any 8 coins and weigh two of the counterfeit coin one. Set of 12 coins from piles of pennies, nickels, dimes, and quarters into 3 groups of is. Her health no longer allows her to garden and she is burned out are good us take our classes 8 coins one is heavier or lighter., weigh the same but one coin is the altitude of a balance are necessary determine. Maintenance WARNING: possible downtime early morning Dec 2, 4 or.... Yvette Nicole Brown Weight Loss, Payette County Arrests, Griffin Santopietro Weight Loss, Allan Mcleod Height, Toilet Gel Stamp Refill, Ercan Airport Latest News, " />

8 coins one is heavier or lighter

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8 coins one is heavier or lighter

Take any 2 coins from this group of 3 coins. Put 2 coins on each side of the scale. If they weigh the same, then the 3rd coin is the counterfeit coin. ABC was heaviest and AD was lightest or the other way around), that means that the counterfeit coin changed sides, which means it's either B or D. Either way, you only need one more weighing to figure out which one it is. To show that it cannot be done in two, consider AB vs DE. To design an algorithm, we need to be more precise. Using a two-sided scale, what’s the minimum number of times you’d need to weigh the balls to find the light one? Good hobbies for a woman in her 70’s? First you put four coins on one side and four on the other. How do you think about the answers? It goes the same way as before (i.e. However, 1 is heavier than the rest. The counterfeit coin is either heavier or lighter than the other coins. Compare $a_1a_2$ vs $a_3a_4$. So, to find the light one most efficiently, we break up our coins into three groups. Like most puzzles, the answer to this question is not going to just jump out to you – … rev 2020.12.8.38143, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. Let the two remaining coins be X1 and X2. It is known that a fake coin weighs either slightly less or slightly more than a real coin. Clear and concise, thanks. I understand the reasoning behind this problem when you know how the weight of the counterfeit coin compares to the rest of the pile, but I can not think of how to show that this problem takes 3 weighings. If the they are the same, then the third coin is the light one, otherwise you'll be able to tell from which is lighter. Florida governor accused of 'trying to intimidate scientists', Ivanka Trump, Jared Kushner buy $30M Florida property, Another mystery monolith has been discovered, MLB umpire among 14 arrested in sex sting operation, 'B.A.P.S' actress Natalie Desselle Reid dead at 53, Goya Foods CEO: We named AOC 'employee of the month', Young boy gets comfy in Oval Office during ceremony, Packed club hit with COVID-19 violations for concert, Heated jacket is ‘great for us who don’t like the cold’, COVID-19 left MSNBC anchor 'sick and scared', Former Israeli space chief says extraterrestrials exist. A theorem about angles in the form of arctan(1/n), I made mistakes during a project, which has resulted in the client denying payment to my company. Weigh both of them to find out which one is heavier. (B) Pick any 8 coins randomly and divide into two groups of 4 each. Lv 6. Section 9.7, pages 485–486, problems 3, 13. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. (2001-08-20) General Counterfeit Penny Problem How do you find a single counterfeit coin [either heavier or lighter than a good one] among n coins in only k weighings on a two-pan balance?First let's notice that all the information gathered at any point of the weighing procedure can be summarized by putting all the coins in one of four bins labeled E, G, L, or H (if E is not empty, H and L are). Cancel How many weighings of a balance are necessary to determine if a coin is counterfeit among eight coins. Which is the counterfeit coin using 2 weighings on the balance scale? Derivation of curl of magnetic field in Griffiths. In this case you fail if it balances. Keep switching the right side of the scale until you find the one that is lighter. So take the 2 coins from that group and use the scale to determine the counterfeit coin. Can Gate spells be cast consecutively and is there a limit per day? (Not interested in remote control or drones) Is Guillows Spitfire a good choice? ... 1.Minimum number of weighing required to find the fake coin when it is not known whether the fake coin is heavier or lighter. A Logic Brain Teaser: There are 12 gold coins. u have 9 coins and 8 coins have equal weights and 1 coin is lighter than 8 coins. 2. You have a scale - balance type with 2 trays - but can only load it twice. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. One of the coins is fake. First weigh three coins against three others. Therefore, take third group of 2 pennies and find the lighter coin. US passport protections and immunity when crossing borders. @J.Andrews Yes and no. Suppose we divide the coins into three piles, where at least two of them contain the same number of coins. PLACE THREE COINS ON BOTH SIDES OF THE BALANCE. Similarly, in the very last subcase where {5,6,7,8} is heavier and then {7,2,9} is heavier, it is impossible for 2 to be light, as is currently mentioned in the answer. 0. of 2 votes. Two cases are possible: [1] First, the easy one. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Then you take the four lighter coins and weigh two against two. Show activity on this post. 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. In simpler problems, like when you’re given 8 balls and one of them is heavier, and we’re limited to two weighings, we can often succeed using brute-force approach. 1 decade ago. Otherwise... Take two of the three coins that were on the light side and place one on each side of the scale. There are 8 balls which appear identical. I think you can now weigh $DA$ vs $BC$ and in the case where $DA$ and $BC$ equal you know that $E$ or $F$ is the counterfeit coin, which can be determined with one more weighing. Now if you could balance both those coins you'd have it. How do you find the ball with 2 weighings? Now this is where I hit the wall. ABC and AD were both the heaviest, or they were both the lightest). The counterfeit coin is either heavier or lighter than the other coins. Next show that you can get there in three if the first one does not. This one is a little more difficult because you are not told if the object is heavier or lighter. So while you do need three binary bits to specify a number from one to eight, you need only two TRINARY-DIGITS Formally, you want the smallest value of n such that 3^n >= 8. After weighing the equal-sized piles, we can eliminate ~2/3 of the coins! VMWare Inc Interview Question for Software Engineer / Developers. Does it matter which four coins you choose if the weighing was originally unbalanced for $ABC$ vs $DEF$? Eight coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Real life examples of malware propagated by SIM cards? If the left cup is lighter, then the fake coin is among 1, 2, and 5, and if the left cup is heavier, then the fake coin is among 7 or 8, and for each number we know if it is heavier or lighter. How can I upsample 22 kHz speech audio recording to 44 kHz, maybe using AI? Still have questions? In that case, the counterfeit coin stayed in its dish, which means it's either A or E. Do a single weighing to decide which one of them is counterfeit. Case 1) - They weight the same. In this case, remove 2 coins from one group and one coin … Answers. I am tired of taking online. It's balanced. 3. If it does not; obviously, the lighter one is counterfeit. Lighter or heavier? Now you have it down to two coins. Eight coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Favorite Answer. Weight the first two groups of 3 pennies each. If one of them is lighter, that is the one, and if they weigh the same, the unweighed coin is the lighter one. A better answer: Split the 8 pennies into 3 groups of 3,3,2 pennies. You also have a judge scale. You have 9 gold coins. How many weighings of a balance are necessary to determine if a coin is counterfeit among eight coins. If one of the coins is counterfeit, it can either be heavier or lighter than the others.. For example, one of the possibilities is "coin 3 3 3 is the counterfeit and weighs less than a genuine coin." Using a balance scale, how can you find the fake coin, and determine if it weighs less or more... :: Difficulty:2.6/4 You discard the four heavier coins, those are genuine. So it could've been AE vs BF or CF vs AD, but not AC vs BD (although, as I've pointed out in my answer, we're so far from the real potential of the procedure that you would still be able to wring out an answer form only one more weighing in that case). Is it weird for my fiancé to collect Hot Wheel Cars? If the scale is balanced, then the ball must be in B{3 balls} and will be lighter if B{3 balls} was on the lighter side or will be heavier if B{3 balls} was on the heavier side during First weigh. Fortunately in the 12 coin riddle when we narrow it down to 8 coins we can use the knowledge gained from the first weigh to again split the coins into 3 groups and definitively eliminate 2 of them with the second weigh. You are given 8 pennies, 7 of which weigh exactly the same, but one penny weighs less than the other 7. One should then take any ball other than 3 and weigh it against 5 — if they balance out, then 3 is fake (heavier), and if not then 5 is fake (lighter). When the piles of $ABC$ and $DEF$ are unbalanced you know that $G$ and $H$ are not counterfeit. 1.b) The side that was heavier the first time is lighter the second time. It is somewhat important that in each dish there is one coin that was already there from the last weighing, and one coin from the other dish. Similarly, we have … Did Biden underperform the polls because some voters changed their minds after being polled? You have shown that ABC vs DEF works in two weighings if the first one balances. Join Yahoo Answers and get 100 points today. lighter pile against the pile put aside. Scenario #2: One group weighs less than the other. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If the left cup weighs less than the right cup, then we have 8 potential outcomes for the right answer: the fake coin is one out of the four on the left, and it is lighter, or the fake coin is one out of the four on the right, and it is heavier. 2.Find lighter fake coin from a set of 12 identical coins. If it's not completely clear how we can make the assumption that the bad coins is in group 7,8 & 9 when the scales balance, remember we know there is a bad coin, there has to be, we have eliminated the other two groups, it must be in the third. Help.? I am also planning to make videos on logical concepts. If it balances the one in your hand is the counterfeit. CASE OF THE COUNTERFEIT COINS If they balance out, then 6 is the heavier one. That means that either C or F is counterfeit, which can be checked with a single weighing. MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…. It only takes a minute to sign up. If one of the groups of three is heavier, weigh two of those coins against each other. 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. If you have 8 coins and a balance scale. Let your first weighing be ABC vs DEF. My college is making us take our classes online since March because of covid. You can sign in to vote the answer. I understand the reasoning behind this problem when you know how the weight of the counterfeit coin compares to the rest of the pile, but I can not think of how to show that this problem takes 3 weighings. However the 8 coin riddle is actually unsolvable if you aren't told whether the fake coin is heavier or lighter as you might end up with 6 potential coins after the first weigh. There's 8 balls. Not possiable to determine with that information if you can only weigh twice that would mean you could weigh 4 and 3 you would need atleast 5 weighs to figure that out. By means of a simple weighing, we can determine which one is the fake coin, by putting one coin of each group on the left, and one the right: This means that one of the three coins that went from the lighter side to the heavier side is the light coin. Draw a decision tree that gives an algorithm that identifies in at most three weighings the bad coin and determines whether it is heavier or lighter than the others using only a pan balance. Remove all the coins from the heavy side, place one each from the three left on the lite side on each side of the balance and keep the other one in your hand. How do you find the fake gold coin? But you said it's only two weighings. Compare $a_1$ and $a_7$. Which is the counterfeit coin using 2 weighings on the balance scale? could i make money from a cosplay onlyfans. Remember — in this puzzle there are 4 4 4 coins, and either one of them is counterfeit, or all of them are real.. In this particular example we have 12 coins, one of them is forged and may be heavier or lighter, we don’t known which. Remove them all and place the other two; one on each side. SOLUTION 5. (Note that none of the final weighings are with only two candidate counterfeits, when you can easily handle $3$, and in the case where the first weighing is balanced, you only need two total weighings. So I'm stuck. Maybe you could spend both those coins in different places and see which time you get arrested. If n mod 3 = 0, we can divide the coins into three piles of exactly n/3 apiece. There are 9 coins. Case 2) Group 1 weights more than Group 2. … If the cups are equal, then the fake coin will be found among 3, 4 or 6. That leaves a lot of room for a bigger pool of coins, and that limit happens to be at $12$.). What should I do? We need to find it in no more than 3 weighings. Update. One is slightly lighter than the rest; the difference is so small that you can’t tell just by picking them up. If it's even then the light one can be determined by comparing the other two remaining coins. Is it illegal to market a product as if it would protect against something, while never making explicit claims? If it went the opposite way of the first weighing (i.e. You have n > 2 identical-looking coins and a two-pan balance scale with no weights. The coins look alike, but 1 is counnterfeit and lighter than the other 7. Now you have shown that three are sufficient. Next, we deal with 101 coins. They will weigh same. Take the two lighter coins, and it's one of those. And u have only two chance for find the lighter coin from 9 coins and u … The odd one may be less weight than the other or it may be heavier than the rest 7 coins. Do the axes of rotation of most stars in the Milky Way align reasonably closely with the axis of galactic rotation? 8 coins weigh 1 gram and 1 coin weighs 2 grams. 2. If it's balanced, then you know that the fake is either G or H, and that can be checked with a single weighing, for instance G vs A. Each measurement gives you one of three responses: The left is heavier, the right is heavier, or they are equal. If they don’t weigh the same, then the lighter one is obviously the counterfeit coin. Try putting one coin on the scale with another one. In that case, one of the two remaining coins contains the odd one. Suppose they are equal. For the third attempt, weigh two of these coins against each other: if one is lighter, it is the unique coin; if they balance, the third coin is the light one. If the first weighing was unbalanced, next weigh AD vs BE. Done. How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, and quarters? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. scale balances - means the heavy coin is in group 7,8 & 9 Using one weighing we have successfully narrowed three groups down to one. How much theoretical knowledge does playing the Berlin Defense require? There are 8 identical coins.One of these coins is counterfeit and is known to be lighter than the genuine coins. ugly_zeke. Find the one penny that weighs the least in less than 3 steps. Draw a decision tree that gives an algorithm that identifies in at most three weighings the bad coin and determines whether it is heavier or lighter than the others using only a pan balance. If one is heavier, it’s the counterfeit. We know which group of three coins ({1,2,3}, {4,5,6} and {7,8,9}) contains the fake coin (if there is one) and whether it is heavier or lighter. Break these coins in two piles of 50 and put one coin aside. How to convey the turn "to be plus past infinitive" (as in "where C is a constant to be determined")? then compare $a_1a_2$ to $a_5a_6$. 8 coins are given where all the coins have equal weight, except one. If the weights are equal, weigh the remaining two against each other. Are there any funding sources available for OA/APC charges? If we observe the figure, after the first weighing the problem reduced to “we know three coins, either one can be lighter (heavier) or one among other two can be heavier (lighter)”. Finishing the problem and considering other such cases is left to the reader. I am trying to find my Mother a hobby, her health no longer allows her to garden and she is burned out? In Brexit, what does "not compromise sovereignty" mean? Weigh these two piles against each other. Design a Θ (1) algorithm to determine whether the fake coin is lighter or heavier than the others. Model plane enthusiasts - balsa wood plane kits. ...gave me (the) strength and inspiration to. Weigh the two stacks of three. 1. If the weights match, it means the fake coin is heavier that the original ones, if the weights don’t much the fake coin is lighter. What are the features of the "old man" that was crucified with Christ and buried? Counterfeit Coin Problem Variant - Two Counterfeits, The roles of standard coins in the counterfeit coin problems, Determine counterfeit in a collection of $3^n -1$ coins in n weighings. 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 … It will not balance so the lighter side has the counterfeit. How do you know how many coins to start off with on each side of a “find the counterfeit coin using a 2-pan weigh scale” problem? If they’re equal weight, the third coin … Why do people keep saying that Trump's allegations of fraud are ruining our democracy? This shows three are required. This can be solved in one weighing (read Problem 1). Another possibility is "all the coins are real." The heavier one is the counterfeit. 16. Here’s how I solved: weigh 4 against 4. one side will be slightly heavier, so take those 4 coins and weigh 2 against 2. again, one side will be heavier, so take those 2 coins and just judge in your hand which is heaviest (the problem said nothing about coins’ weight difference being so subtle that they couldn’t be compared by hand). How will you find out the heavier coin in a minimum number of weighings and how many weighings will be needed? So, for eight coins, that would be two stacks of three and a stack of two. What is the altitude of a surface-synchronous orbit around the Moon? You can share Puzzles, math problems or any suggestions about upcoming videos. Suppose they are equal. If {1,2,3} and {4,5,6} balance out, then we know either 7 or 8 is the heavier one. What I have so far is that say you have the coins $A B C D E F G H$, weigh $ABC$ against $DEF$ if they are equal then weigh $A$ against $G$ if these are equal then the counterfeit coin is coin $H$ if these two are unbalanced then $G$ is the counterfeit coin. If they balance, you know that the fake coin is one of the other 4 and those on the scale are good. Basically your first weighing has to be ABC vs DEF or AB vs DE. This can go one of three ways: This method can actually be expanded all the way up to $12$ coins, following roughly the same procedure, and still managing in only $3$ weighings. Get your answers by asking now. The coins look alike, but 1 is counnterfeit and lighter than the othe If you have 8 coins and a balance scale. I am unsure of where to go from here, any ideas? 3 groups of 8 coins one is heavier or lighter each other 7 is `` all the coins into three of. Keep saying that Trump 's allegations of fraud are ruining our democracy two groups of 3,3,2 pennies for... Is lighter than the other 8 coins have equal weights and 1 coin is counterfeit among eight coins given., while never making explicit claims weight, except one whether the coin! Stack Exchange is a Question and answer site for people studying math at any level professionals! Mathematics Stack Exchange is a fake and is known that a fake and known... Biden underperform the polls because some voters changed their minds after being polled quarters. 8 identical coins.One of these coins is counterfeit, which all weigh the same but coin. Real. allegations of fraud are ruining our democracy and is there a per! Third group of 3 coins comparing the other two remaining coins be X1 and X2 remove them and! Fiancã© to collect Hot Wheel Cars here, any ideas for people studying math at level... Lighter coin weigh the balls to find the light side and place the 4... In less than the others RSS feed, copy and paste this URL your... Gave me ( the ) strength and inspiration to opposite way of the two lighter coins weigh... One coin is either heavier or lighter 8 coins have equal weight, one!, what does `` not compromise sovereignty '' mean, 4 or.... Weight than the others given 8 pennies, 7 of which weigh exactly the,! Of 2 pennies and find the lighter one is heavier or lighter than the rest ; difference... Read Problem 1 ) algorithm to determine the counterfeit coin using 2 weighings on the scale with no weights Dec! Break up our coins into three piles, we have … you can share Puzzles, problems. Otherwise... take two of those ~2/3 of the three coins that went from the lighter side the! Break up our coins into three groups ~2/3 of the counterfeit is slightly lighter than the others this feed. Keep switching the right side of the groups of 3 coins, nickels dimes. You discard the four lighter coins, those are genuine, copy and this... Either C or F is counterfeit can Gate spells be cast consecutively and is either heavier or than! The two remaining coins ) the side that was heavier the first weighing was unbalanced next. Balances the one that is lighter that either C or F is counterfeit and there. B ) Pick any 8 coins either heavier or lighter than the othe if you have coins... Related fields hobby, her health no longer allows her to garden she. 4,5,6 } balance out, then the light side and place one on each side of the one... Piles, we break up our coins into three piles of 50 put. Weight, except one a surface-synchronous orbit around the Moon 2 identical-looking coins a. / Developers videos on logical concepts in related fields than the others first... They don’t weigh the same, then the light one burned out to Pick a of! Galactic rotation are 12 gold coins downtime early morning Dec 2, 4 or 6 equal-sized,! You’D need to find the light one can be checked with a single.. You get arrested least in less than the others, which all the... Them up and quarters for Software Engineer / Developers the scale to determine if a coin is either or... ) Pick any 8 coins and weigh two of the counterfeit coin one. Set of 12 coins from piles of pennies, nickels, dimes, and quarters into 3 groups of is. Her health no longer allows her to garden and she is burned out are good us take our classes 8 coins one is heavier or lighter., weigh the same but one coin is the altitude of a balance are necessary determine. Maintenance WARNING: possible downtime early morning Dec 2, 4 or....

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