ChibiV Posted October 7, 2002 Share Posted October 7, 2002 If you have 12 gold coins, and there's one fake one. You don't know if the fake one is heavier or lighter than the real one. Given: one balance scale (no number or anything) maximum 3 chances to weight question: How do you find out which is the fake one with only 3 chances of weighing it. Link to comment Share on other sites More sharing options...
Dan L Posted October 7, 2002 Share Posted October 7, 2002 That isn't too hard. First, let's say the fake is lighter. First you put 6 coins on each side of the scale. As one is fake, the two groups will be a different weight. The lighter group of 6 has the fake. From the six coins which you know one is fake, put 3 on each side of the scale. Again, the lighter set of 3 will contain the fake. Put two of the three which you know contain the fake on the scale (one on each side). If they are both the same, then the one you didn't weigh is fake, and if one is lighter, then that one is fake. Link to comment Share on other sites More sharing options...
ChibiV Posted October 7, 2002 Author Share Posted October 7, 2002 [QUOTE][i]Originally posted by Deus_Ex_Machina [/i] [B]That isn't too hard. First, let's say the fake is lighter. [/b][/quote] This is the key to the problem, what if the fake one is heavier, you only have 3 chances to get it right, so this won't work. The problem may look simple, but it's not. If you know if the weight of the fake coin, then it's easy, but the point is, you don't know. That's the hard part. Link to comment Share on other sites More sharing options...
ChibiV Posted October 7, 2002 Author Share Posted October 7, 2002 [QUOTE][i]Originally posted by Deus_Ex_Machina [/i] [B]Oops... I failed to read the 'don't' in 'don't know'... sorry.. [/B][/QUOTE] it's OK, it's a good guess though. Link to comment Share on other sites More sharing options...
Dan L Posted October 7, 2002 Share Posted October 7, 2002 Oops... I failed to read the 'don't' in 'don't know'... sorry.. I have a better answer.. You measure three coins each side the first time... Do the same the second time, but replace [i]one[/i] of the groups of 3. If they all weigh the same, then the one you didn't weigh has the fake. the problem is you still don't know if the fake is heavy or light. If, on the other hand, one of the three sets of 3 coins is heavier or lighter, then you know it contains the fake and you also know whether the fake is heavier/lighter. Then, you follow the third step in my original plan. The only problem with that plan is that if the fake isn't one of the 9 coins you measure in step one and two, you can't know which one is fake.. (P.S. to the moderators.. ChibiV didn't double post.. I deleted my last post cos it was really short) Link to comment Share on other sites More sharing options...
MathGuy2 Posted October 7, 2002 Share Posted October 7, 2002 (I'm typing this as I think...) Let's see. Five coins on each side, two still on the table. If the 5+5 balance, balance one of the two against one of the ten (which we know is real). If they balance, the remaining coin is fake. If they don't, then the tested coin is fake. QED in two moves. If the 5+5 don't balance, then take the left side (e.g.) split it into group of 3 on the left, group of 2 on the right. err.....mathematical aside here, what are the unknowns? weights of twelve coins. What are the ....never mind, mind overanalyzed problem. okay, 3 from left on left, 2 from left on right. Pile originally on right kept on right side of table, leftover 2 - take one and put it on the group of two, keep the other behind the balance. If the two groups don't balance, then take the left group against 3 of the "known good" from right of balance...now we know if it's heavier, but there go our tests. Er...let me name the coins, ABCDEFGHIJKL. Split into three groups of 4. Balance ABCD and EFGH. If they balance, balance IJ and KL. wait..........I got it! It's a trick question! The first time you use the balance - alternate putting coins on left and right sides. Every two, watch the balance. When it goes off balance, take one of the last two you balanced with another coin (not the same one that was added that turn). If they unbalance, then that coin's the fake, otherwise, the other one that you didn't test is the fake. no, that can't be the answer....somehow it doesn't seem correct... er...(think) I is (am) heavy fake, ABC DEF/GHI JKL, ABC GHI/DEF JKL, either light fake is in DEF or heavy fake in GHI. so measure DEF against (e.g.) ABC, if they balance fake is in GHI. no!!! one more balance... I frankly don't think the problem can be solved in three moves - you've got too many unknowns (which of [b]12[/b] and unknown light/heavy) and too few knowns (# of balances). I really think it can only be done in four moves. I'll give it to my friends, anyway... Good job in advance to anyone who can solve it (including the person who came up with the riddle, if he/she knew the answer). Link to comment Share on other sites More sharing options...
ChibiV Posted October 7, 2002 Author Share Posted October 7, 2002 hehe, if I post it up, then I must know the answer. There's a way to solve this riddle. Link to comment Share on other sites More sharing options...
Sere Tuscumbia Posted October 7, 2002 Share Posted October 7, 2002 Does this thread have a point? If you really wanted to get this out, you should have put it in your siggie and then had people PM you with the answer. Or made a website, and said something about it in your siggie. I don't think you needed to post this . . . Sere Link to comment Share on other sites More sharing options...
zidane11 Posted October 7, 2002 Share Posted October 7, 2002 [QUOTE][i]Originally posted by Sere Tuscumbia [/i] [B]Does this thread have a point? If you really wanted to get this out, you should have put it in your siggie and then had people PM you with the answer. Or made a website, and said something about it in your siggie. I don't think you needed to post this . . . Sere [/B][/QUOTE] James did give him permission to post this. There isn't anything wrong with it any ways. What's wrong with posting a riddle, there isn't a rule against it. It's a thought provoking thread so it should be just fine with the moderators. I think I'll try and solve the riddle my self. Weigh each six and find out which one is lighter. Then weigh the six coins from that group by half. Which means put three on each side. See the lighter side and see if you can tell a difference between the weight of the coins. I don't any of that made sense but at least I tried. Can you post the answer chibiV? Link to comment Share on other sites More sharing options...
conpiracymonki Posted October 7, 2002 Share Posted October 7, 2002 [b][size=1] A)Weigh four coins, on one side (say 1,2,3,4) and four on the other (5,6,7,8). B)If the balance is equal at (A), then measure 1,2,3 against 9,10,11. C)If balance is still equal at (B), then obviously 12 is the fake coin. Weigh 1/2/3/4/5/6/7/8/9/10/11 against 12 just to see whether it's lighter or heavier... -_-' (or if you have to use 3 measures) D)If 1,2,3 are lighter than 9,10,11 in (B), then weigh 9 and 10 against each other. If one is heavier than the other, it is obviouslt the fake coin. If they're both the same, then the fake is 11. E)If 1,2,3 are heavier than 9,10,11 in (B), then weigh 9 against 10. The lighter one is the fake. If they're equal, then the fake is 11 again. I uh... don't know how to figure it out if 1,2,3,4 are heavier than 5,6,7,8, or are lighter. So I still need to do more thinking....[/b] *head hurted*[/size] Link to comment Share on other sites More sharing options...
Vegitto4 Posted October 7, 2002 Share Posted October 7, 2002 What goes up a pipe down, but not down a pipe up? The winner gets a cookie Link to comment Share on other sites More sharing options...
zidane11 Posted October 7, 2002 Share Posted October 7, 2002 [QUOTE][i]Originally posted by Vegitto4 [/i] [B]What goes up a pipe down, but not down a pipe up? The winner gets a cookie [/B][/QUOTE] The itsy bitsy spider maybe? I'll try and think of some other answers in the mean time. Link to comment Share on other sites More sharing options...
MathGuy2 Posted October 7, 2002 Share Posted October 7, 2002 Vegitto4 - maybe someone goes "up the wall" unless someone else "pipes down", but not "down the wall" unless they "pipe up"? Something like that? ChibiV, check your answer [i]carefully[/i] - unless it's a trick question. I seriously think it can't be done. What 11-letter English word describes toothpaste on the floor? (it's kind of a joke) Link to comment Share on other sites More sharing options...
conpiracymonki Posted October 7, 2002 Share Posted October 7, 2002 [b][size=1] Toothpasted? I have no idea >.<[/b][/size] Link to comment Share on other sites More sharing options...
Darkmoon Posted October 7, 2002 Share Posted October 7, 2002 [QUOTE][i]Originally posted by Vegitto4 [/i] [B]What goes up a pipe down, but not down a pipe up? The winner gets a cookie [/B][/QUOTE] I've got three guesses for this one: 1) A very annoying person that won't stop talking 2) A voice 3) Some kinda sound maybe?? If I'm wrong then can you tell me if I "missed it by a mile" or even a little close to the answer? Link to comment Share on other sites More sharing options...
Corey Posted October 7, 2002 Share Posted October 7, 2002 [b]To the gold riddle:[/b] Screw the scales. Bite each coin and see if your teeth marks are there. Link to comment Share on other sites More sharing options...
Deedlit Posted October 8, 2002 Share Posted October 8, 2002 [color=green]lol That's one way of determining the answer. I'll give a try at the pipe riddle. Is it one of those tools they use to make sure a board or something is level? You know, it's a tube that has water in it, but it also has an air bubble. When you tilt the tube downwards, the air bubble goes up. When you tilt it up, the air bubble goes the down. Am I right, close, or a million miles from it?[/color] Link to comment Share on other sites More sharing options...
Juu Posted October 8, 2002 Share Posted October 8, 2002 [color=deeppink] [size=1]mkay, here's a favorite ^^ I...don't think they're [i]too[/i] hard to figure out.. Easy: Two fathers and two sons went fishing. Everyone caught a fish. But there were only three fish. How is this possible? Medium: There was a man that had to live in a box. He couldn't escape, it was just.. a box. There was only a bed, and a calendar. But he survived. How is this possible? (hint: It has nothing to do with him escaping) Medium hard: There was a boy, that was selling some mushrooms one day. When night fell, he grew tired, and went to sleep. He hid the money he earned by his side, and fell asleep. When he woke up, his money was gone! He immediately went to a guard by the palace he was selling them by, and told them what had happened. Then the guard ordered everyone that was there at the time his money was stolen. He then told everyone to get a magical stick of truth from a basket, so everyone did. He told everyone to stick their sticks out from a wide circle. He said the stick of the beholder who stole the money, would grow out into the center, revealing the theif. Everyone reached out their sticks. Immediately, the guard grabbed the shortest stick and exclaimed. That's the theif! She's the one that stole the money! How did they know? Medium: There was a man who had been kind all his life. So one day, right before he died, the man was granted one wish, and that was to see what heaven and hell looked like. His wish was granted. First he went to hell. There were four men sitting at a square table, on the ground, who looked starving. The men were sitting one foot away from the table, with chopsticks that were three feet long. No matter how hard they tried, they couldn't get the food in their mouth. Then the man went to heaven. He was surprised to see the men in heaven were sitting the same way! They also had three foot chopsticks, yet they were not starving! They were all eating happily, with satifying glances. Why were the people in heaven not starving? (hint: Everything was exactly the same as hell, yet they were not starving. They all knew how to use chopsticks.. and it has nothing to do with magic) Figure those out. ^_^ It took me quite a while to get those..like.. four years ago. ^^;[/color] [/size] Link to comment Share on other sites More sharing options...
Sui Generis Posted October 8, 2002 Share Posted October 8, 2002 [quote]Medium: There was a man who had been kind all his life. So one day, right before he died, the man was granted one wish, and that was to see what heaven and hell looked like. His wish was granted. First he went to hell. There were four men sitting at a square table, on the ground, who looked starving. The men were sitting one foot away from the table, with chopsticks that were three feet long. No matter how hard they tried, they couldn't get the food in their mouth. Then the man went to heaven. He was surprised to see the men in heaven were sitting the same way! They also had three foot chopsticks, yet they were not starving! They were all eating happily, with satifying glances. Why were the people in heaven not starving? (hint: Everything was exactly the same as hell, yet they were not starving. They all knew how to use chopsticks.. and it has nothing to do with magic)[/quote] Easy the people in hell are too selfish and ignorant to think of others. They sat 2 to a side. They tried to feed themselves not others. The people in heaven loved eachother so they fed eachother with the chopsticks. Link to comment Share on other sites More sharing options...
Jeebs Posted October 8, 2002 Share Posted October 8, 2002 The 1st one (Juuthena): There were only 3 people: a boy, his father, and his grandfather. The father was the boy's father and the grandfather was the father's father. The boy was the father's son and the father was the grandfather's son. (2 fathers, 2 sons) Last one: The people in hell didn't have mouths. Link to comment Share on other sites More sharing options...
zidane11 Posted October 8, 2002 Share Posted October 8, 2002 The last one of Juuthena's. Maybe the food was closer to the edge of the table in heaven. I hope that's right. Link to comment Share on other sites More sharing options...
Juu Posted October 8, 2002 Share Posted October 8, 2002 [color=deeppink] [size=1]Lessee... Bryan, you got number four correct, and Shadow, you got number one correct. ^_^ *hands bryan a marshmellow* *hands shadow $10* @_@[/color] [/size] Link to comment Share on other sites More sharing options...
conpiracymonki Posted October 8, 2002 Share Posted October 8, 2002 [b][size=1] Juuthena, can you please explain the mushroom one again? I don't understand it.. Thanks[/b] OMG, someone else with a Grr avatar :updown:[/size] Link to comment Share on other sites More sharing options...
Sui Generis Posted October 8, 2002 Share Posted October 8, 2002 Hm...I'll try the semi-hard one.... Its a complete guess The girl with the shortest stick was the theif because she knew it would grow so she did not fully extend her arm where as the other people did. she did this to cover it up so when it grew it would be as long as the others. The boy and the gaurd expected this and saw that her arm was bent more than the others letting them know that the stick grew and she was trying to hide.... Complete guess... Here's an easy one: A man and his son are in a car accident. They are both rushed to the hospital. The father and son have different doctors. As the son goes in for surgery the doctor turns around and sees him. The doctor then exclaims "I can't operate on this boy he is my son." How is this possible? Link to comment Share on other sites More sharing options...
Deedlit Posted October 8, 2002 Share Posted October 8, 2002 [color=green]That sounds right to me, Bryan. ^_^ As for your second riddle, the answer is that the doctor was a nurse.[/color] Link to comment Share on other sites More sharing options...
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