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Contest 10 - Three Logic Questions with a Twist (Ended)
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Scott (Admin) RJ: Ratan Joyce CO: Ratan Joyce Post Rating: 0 + / - Total Posts: 1175 Karma: 5083 Joined: Jan 13, 2012 |
Posted on Apr 20, 2012 (Last edited on Apr 20, 2012) Contest ended early... once again my attempt to outwit the players has failed miserably.Results: Ultimate Evil Logician: Innocent Bystander (2000 influence + 1000 influence for pointing out the loophole in the rules) Master Mimic: David Archer (1000 influence) Master Logician: Walter Yorkshire (1000 influence) Apprentice Logician: James Grey (500 influence) Timeline: Innocent Bystander: 1, 2 correct David Archer: 1 correct Walter Yorkshire: 1, 2 correct Galaga Galaxian: 1 correct James Grey: 1, 2 correct Innocent Bystander: All 1, 2, 3 correct David Archer: 1, 2, 3 correct --------------------------------------------------------- - ORIGINAL CONTEST Description: I'll post 3 logic questions (if you are stuck, some of the answers may be found on the net), and the influence rewards will be given in a special way. Rewards: 1. First to answer all 3 questions correctly will be rewarded 2000 influence! 2. Second to answer all 3 questions correctly will be rewarded 1000 influence. 3. First to answer 2 questions correctly will be rewarded 1000 influence. 4. Second to answer 2 questions correctly will be rewarded 500 influence. 5. No influence given for participation. EDIT: Each person can only get 1 reward The Twist: 1. You must submit your answer in a post as a reply to this thread. So once posted, your submission is available for everyone else to see/copy. If you had 2 correct answers, and 1 wrong answer, someone else can simply copy your correct answers, and if (s)he answered the other question correctly, (s)he gets the top prize. 2. Editing your post automatically voids your entry. But you may delete your post and repost it. Reason being I don't want to make a function to sort the posts by their edit time. 3. You may ask for clarifications on the problems (by PM or by posting), and I will add them into the clarification part of this post. But I will not comment on the answers until the deadline of the contest. Deadline: Sunday, Apr. 22, 6:00 P.M. Now, the Problems: Q1. 4 Switches and a Lamp You are in a room (Room A) with four switches (A, B, C, D), and you know there is a table lamp (using an incandescent light bulb) in the next room (Room B) controlled by one of the switches in Room A. Your task is to discover which one. You can’t see whether the light is on or off from Room A, and once you leave Room A, you are not allowed to come back. You may turn any number of switches on or off, any number of times you want. How would you find out which switch turns the light on? Q2. Strange Island There is a strange island in Eosia with 50 blue-eyed people and 50 brown-eyed people. They are all perfect logicians. No one knows the color of their eyes, but everyone knows they can only have blue eyes or brown eyes. Every night at midnight, a ferry stops at the island. If anyone has figured out the color of their own eyes, they must leave the island that midnight. Everyone on the island knows the rules (but are not given the total numbers) and is constantly aware of everyone else's eye color. Everyone keeps a constant count of the total number they see of each (excluding themselves). However, they cannot otherwise communicate. So any given blue-eyed person can see 50 people with brown eyes and 49 people with blue eyes, but that does not tell them their own eye color; it could be 51 brown and 49 blue. On his vacation Ratan Joyce landed on the island and said in front of everyone: "I can see someone with blue eyes." Since Ratan Joyce only tells the truth, everyone believes him. Now, the question is, who leaves the island, and on which night(s)? (Excluding Ratan Joyce) Q3. Liars and Truth-tellers There are two islands in the middle of the ocean. According to your Eosia Travel Guides which can be trusted, one island is inhabited by liars who only tell lies, and the other island is inhabited by truth-tellers who only speak the truth. Furthermore, one island has an even number of inhabitants above 100 (e.g. 100, 102, 104, ...), and the other has an odd number of inhabitants above 100 (e.g. 101, 103, 105, ...) There is a statue of Ratan Joyce on the island with an even number of inhabitants. You happened to land on one of the islands, not knowing which, and want to find out if the RJ Statue is on the island you landed on. What is the minimal number of simple questions you have to ask to find this out, and what is(are) the question(s)? Everyone on the two islands know everyone else, but they are all poor logicians and therefore can only answer the simplest questions: "Q: How many people live on the other island?" -> "99" "Q: What would the people on the other island answer if I ask them which island has the RJ Statue?" -> "I don't know, this question is too hard." Clarifications: Do the brown-eyed dudes know if the blue-eyed dudes left when they are leaving, or do they figure it out the day after? The day after |
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Innocent Bystander RJ: Matthew Matician Post Rating: 0 + / - Total Posts: 76 Karma: 54 Joined: Apr 2, 2012 |
Posted on Apr 20, 2012 1) Turn on switch A and B for an hour, then turn off switch B and turn on switch C. Move rooms quickly and touch the light. If the light is:On & very hot: switch A turns light on. Off & very hot: switch B turns light on. On & not very hot: switch C turns light on. Off & not very hot: switch D turns light on. 2) Everyone with blue eyes will depart on the 50th night. All brown-eyed people depart on the 51st night. 3a) If this isn't too tricky of a question, you can do it in one: "What would you have told me if I asked you an hour ago: 'Are there an even number of people on this island?'" If they say, "I would have told you 'yes'" (or some variation), then the statue is on this island; if 'no' then the statue is on the other island. 3b) If (3a) is too "tricky", I can see doing it in two questions: q1) How many people live on both islands combined? q2) How many people are on this island? If they answer even for both or odd for both, they are liars. If they answer odd for one and even for the other, they are truth-tellers. Based on that information, you can discern the truth from q2: If they are truth-tellers, and the answer to q2 is 'even': statue is on this island. truth-tellers and answer is 'odd': statue is on other island. liars and answer is 'even': other island liars and answer is 'odd': this island. --- Hopefully I didn't get any off-by-ones in the answers. :) |
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Innocent Bystander RJ: Matthew Matician Post Rating: 0 + / - Total Posts: 76 Karma: 54 Joined: Apr 2, 2012 |
Posted on Apr 20, 2012 A clarification: for (2), I'm assuming people sleep and that they aren't aware of who boards the ferry until the next morning (or at least until the ferry leaves).If everyone is paying attention to who gets on the ferry, then as soon as the first person walks onto the ferry (on the 50th night), all brown-eyed folks will realize that their eye color, too. |
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David Archer RJ: BallC CO: BallC Post Rating: 0 + / - Total Posts: 142 Karma: 135 Joined: Apr 11, 2012 |
Posted on Apr 20, 2012 Q1:Turn on switches C,D - wait 15 minutes Turn off switch C, turn on switch B Enter Room B If bulb is unlit and cool, switch A If bulb is lit and cool, switch B If bulb is unlit and warm, switch C If bulb is lit and warm, switch D Q2: N=1, 1 leaves on 1st night N=2, 2 leave on 2nd night ... N=50, 50 leave on the 50th night All 50 blue-eyed people leave on the 50th night. Q3: Two questions 1: I am on this island 2: Is the statue on this island |
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Control Volume RJ: ControlVolume CO: Control Volume Post Rating: 0 + / - Total Posts: 43 Karma: 122 Joined: Mar 31, 2012 |
Posted on Apr 20, 2012 Clarification: do the brown-eyed dudes know if the blue-eyed dudes left when they are leaving, or do they figure it out the day after?e: darn, looks like people beat me to the answers anyways. |
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Walter Yorkshire RJ: Walter Yorkshire CO: Walter Yorkshire Post Rating: 0 + / - Total Posts: 132 Karma: 379 Joined: Feb 5, 2012 |
Posted on Apr 20, 2012 1) Turn on switch A and B for an hour, then turn off switch B and turn on switch C. Move rooms quickly and touch the light. If the light is:On & very hot: switch A turns light on. Off & very hot: switch B turns light on. On & not very hot: switch C turns light on. Off & not very hot: switch D turns light on. 2: On the 50th night, everyone with blue eyes leave On the 51st night, everyone with brown eyes leave 3: Two questions 1: Am I on this Island 2: Is the statue on this Island |
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Galaga Galaxian RJ: Galaga Galaxian Post Rating: 0 + / - Total Posts: 6 Karma: 28 Joined: Apr 18, 2012 |
Posted on Apr 20, 2012 Q1. Well, assuming I'm not allowed to use an electrical tools or check the wiring... (I am an electrician)I Turn on switch A After twenty or thirty minutes, I turn off switch A and turn on switch B. After only one minute, I turn off switch B, turn on Switch C and RUSH to the other room. If the light bulb is: Off, Blistering Hot; it is probably Switch A Off, Warm: It is Switch B On: It is Switch C Off, Cold: It is Switch D Q2. I need to work on. Q3. I ask only Two questions. The first a simple yes/no question or basic math problem. EG: "Is the sky blue?" or "What is two plus two"? This will easily establish if they're truthful or liars. After that its just a matter of asking about the statue. |
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Galaga Galaxian RJ: Galaga Galaxian Post Rating: 0 + / - Total Posts: 6 Karma: 28 Joined: Apr 18, 2012 |
Posted on Apr 20, 2012 Holy crap some of you are fast. :(
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James Grey RJ: Dairy Aire CO: Dairy Aire Post Rating: 0 + / - Total Posts: 26 Karma: 21 Joined: Apr 17, 2012 |
Posted on Apr 20, 2012 Turn switch A on, wait 17 minutes, turn switch B on, wait 3 minutes, turn C on while turning A and B off. Go into the next room. If the Bulb is on, the switch is C, if the bulb is off but very hot it's switch A, if it's mildly hot it's switch B, if it's room temperature it's switch D.On the 50th day all 50 blue eyed people will leave (Long explanation cba :P) Two questions, how many people are on both islands? If he gives an odd number he's the truth teller if he gives an even one he's the liar. Then can ask how many people are on this island, if evan I'm on the right one :D If odd go to the other one. |
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James Grey RJ: Dairy Aire CO: Dairy Aire Post Rating: 0 + / - Total Posts: 26 Karma: 21 Joined: Apr 17, 2012 |
Posted on Apr 20, 2012 2) Brown eyed will leave the next day :)
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Innocent Bystander RJ: Matthew Matician Post Rating: 0 + / - Total Posts: 76 Karma: 54 Joined: Apr 2, 2012 |
Posted on Apr 20, 2012 1) Turn on switch A and B for an hour, then turn off switch B and turn on switch C. Move rooms quickly and touch the light. If the light is:On & very hot: switch A turns light on. Off & very hot: switch B turns light on. On & not very hot: switch C turns light on. Off & not very hot: switch D turns light on. 2) Everyone with blue eyes will depart on the 50th night. All brown-eyed people depart on the 51st night. 3 revisited) One question: "Are there an even number of truth tellers?" Four cases: You landed on Even & truth-tellers: they will tell you 'yes' You landed on Even & liars: they will tell you 'yes' You landed on Odd & truth: they will tell you 'no' You landed on Odd & liars: they will tell you 'no' The statue is on your island if and only if they say 'yes' |
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Innocent Bystander RJ: Matthew Matician Post Rating: 0 + / - Total Posts: 76 Karma: 54 Joined: Apr 2, 2012 |
Posted on Apr 20, 2012 <logician>Assuming all 3 are correct, posting twice as a safeguard in case Ratan can be convinced that I am the second (as well as the first) to post all 3 solutions.</logician>
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Innocent Bystander RJ: Matthew Matician Post Rating: 0 + / - Total Posts: 76 Karma: 54 Joined: Apr 2, 2012 |
Posted on Apr 20, 2012 1) Turn on switch A and B for an hour, then turn off switch B and turn on switch C. Move rooms quickly and touch the light. If the light is:On & very hot: switch A turns light on. Off & very hot: switch B turns light on. On & not very hot: switch C turns light on. Off & not very hot: switch D turns light on. 2) Everyone with blue eyes will depart on the 50th night. All brown-eyed people depart on the 51st night. 3) One question: "Are there an even number of truth tellers?" Four cases: You landed on Even & truth-tellers: they will tell you 'yes' You landed on Even & liars: they will tell you 'yes' You landed on Odd & truth: they will tell you 'no' You landed on Odd & liars: they will tell you 'no' The statue is on your island if and only if they say 'yes' |
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David Archer RJ: BallC CO: BallC Post Rating: 0 + / - Total Posts: 142 Karma: 135 Joined: Apr 11, 2012 |
Posted on Apr 20, 2012 1) Turn on switch A and B for an hour, then turn off switch B and turn on switch C. Move rooms quickly and touch the light. If the light is:On & very hot: switch A turns light on. Off & very hot: switch B turns light on. On & not very hot: switch C turns light on. Off & not very hot: switch D turns light on. 2) Everyone with blue eyes will depart on the 50th night. All brown-eyed people depart on the 51st night. 3) One question: "Are there an even number of truth tellers?" Four cases: You landed on Even & truth-tellers: they will tell you 'yes' You landed on Even & liars: they will tell you 'yes' You landed on Odd & truth: they will tell you 'no' You landed on Odd & liars: they will tell you 'no' The statue is on your island if and only if they say 'yes' |
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Galaga Galaxian RJ: Galaga Galaxian Post Rating: 0 + / - Total Posts: 6 Karma: 28 Joined: Apr 18, 2012 |
Posted on Apr 20, 2012 Funny thing is, for the first question, my original idea was to just turn one switch on/of really, REALLY fast for a while to make the bulb burn out. But I realized that'd only work with 3 switches, then I realized the heat of the bulb could be a solution.Still, looks like people found a slightly more streamlined version of the solution (turn two switches on at once). |
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Scott (Admin) RJ: Ratan Joyce CO: Ratan Joyce Post Rating: 0 + / - Total Posts: 1175 Karma: 5083 Joined: Jan 13, 2012 |
Posted on Apr 20, 2012 Madness... contest ended early :-(You all know why. If I were to do this again I'd need to give out 5 different questions, none of which with answers available. |
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