Twelve Pills
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Agent
Member # 5814
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written Sunday, April 9 2006 20:15
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You have twelve pills. One of them is different only in weight. It may be either lighter or heavier. You also have a scale. It may be used three times. Find the different pill. -------------------- quote: Posts: 1115 | Registered: Sunday, May 15 2005 07:00 |
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Lifecrafter
Member # 6700
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written Sunday, April 9 2006 20:24
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You do realize that the instant somebody gets this, they'll post it and ruin it for everyone else. -------------------- The Silent Assassin is calling for an Admin to lock this one, pronto, so that he can figure it out for himself! -------------------- -Lenar Labs What's Your Destiny? Ushmushmeifa: Lenar's power is almighty and ineffable. All hail lord Noric, god of... well, something important, I'm sure. Posts: 735 | Registered: Monday, January 16 2006 08:00 |
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BANNED
Member # 4
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written Sunday, April 9 2006 20:25
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Question- How accurate is the scale? Because it'd be really friggin' obvious if it would tell us exact weights, but if it only did "heavier/lighter," that'd change things. -------------------- * Posts: 6936 | Registered: Tuesday, September 18 2001 07:00 |
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Infiltrator
Member # 3441
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written Sunday, April 9 2006 20:27
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This is going to be one of those things where I kick myself for not finding the answer. EDIT: Is this a scale or a balance? [ Sunday, April 09, 2006 20:28: Message edited by: Smugglers' Alliance, Chief of the ] -------------------- "As our circle of knowledge expands, so does the circumference of darkness surrounding it." --Albert Einstein -------------------- Posts: 536 | Registered: Sunday, September 7 2003 07:00 |
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Shaper
Member # 247
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written Sunday, April 9 2006 21:06
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I've heard this one multiple times. But I don't remember the answer. I probably never figured it out the last times. Any way here is a possible answer: Answer don't look if you really want to figure it out yourself. [ Sunday, April 09, 2006 21:11: Message edited by: VCH ] -------------------- The Knight Between Posts. Posts: 2395 | Registered: Friday, November 2 2001 08:00 |
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? Man, ? Amazing
Member # 5755
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written Sunday, April 9 2006 22:11
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I remember puzzling over that one for a long time, about 20 years ago. It seems fairly pedestrian now. While cogitating, try this one out. From the letters in the word "Pythagorean" create two words that use up all the letters. The words must be math related. -------------------- quote: Posts: 4114 | Registered: Monday, April 25 2005 07:00 |
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Infiltrator
Member # 6652
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written Monday, April 10 2006 01:15
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EDIT AGAIN: Oops. Nevermind [ Monday, April 10, 2006 01:26: Message edited by: Wonko The Sane ] -------------------- But I don't want to ride the elevator. Posts: 420 | Registered: Sunday, January 8 2006 08:00 |
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Lifecrafter
Member # 6403
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written Monday, April 10 2006 01:22
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Sure that works only if one pill is heavier, but he said heavier or lighter. -------------------- ??? ?????? ???? ????? Posts: 883 | Registered: Wednesday, October 19 2005 07:00 |
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Infiltrator
Member # 6652
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written Monday, April 10 2006 01:25
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Oops. Sorry, didn't see that. -------------------- But I don't want to ride the elevator. Posts: 420 | Registered: Sunday, January 8 2006 08:00 |
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Raven v. Writing Desk
Member # 261
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written Monday, April 10 2006 04:03
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I assume this has got to be a balance, and not a scale -- it doesn't seem even remotely possible with a single plate scale. -------------------- Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560 | Registered: Wednesday, November 7 2001 08:00 |
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Shaper
Member # 32
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written Monday, April 10 2006 04:36
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quote:Two words that together contain all the letters, or two separate words which are permutations of Pythagorean? -------------------- Lt. Sullust Cogito Ergo Sum Polaris Posts: 2462 | Registered: Wednesday, October 3 2001 07:00 |
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Raven v. Writing Desk
Member # 261
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written Monday, April 10 2006 04:51
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Ooh, got it. Pythagorean = SPOILER -------------------- Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560 | Registered: Wednesday, November 7 2001 08:00 |
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Guardian
Member # 6670
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written Monday, April 10 2006 06:55
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I've done something similar before. The spoiler, if anyone wants it, in incremental steps: (If you feel tempted to look, blame yourself, not me.) SPOILER1 SPOILER2 SPOILER3 SPOILER4 SPOILER5 Does anyone remember the "water-from-the-well" one? (Get one litre when you have two buckets of size...") -------------------- IF I EVER BECOME AN EVIL OVERLORD: If I must have computer systems with publically available terminals, the maps they display of my complex will have a room clearly marked as the Main Control Room. That room will be the Execution Chamber. The actual main control room will be marked as Sewage Overflow Containment. Posts: 1509 | Registered: Tuesday, January 10 2006 08:00 |
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Nuke and Pave
Member # 24
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written Monday, April 10 2006 08:13
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quote:Your solution assumes that you know that bad pill is heavier. However, in this version of the puzzle, you have to find out whether the bad pill is heavier or lighter. So here is are hints for adjusting your solution: hint 1 hint 2 [ Monday, April 10, 2006 08:14: Message edited by: Zeviz ] -------------------- Be careful with a word, as you would with a sword, For it too has the power to kill. However well placed word, unlike a well placed sword, Can also have the power to heal. Posts: 2649 | Registered: Wednesday, October 3 2001 07:00 |
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Infiltrator
Member # 3441
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written Monday, April 10 2006 08:48
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I still, can't see it being done with less than four weighings. -------------------- "As our circle of knowledge expands, so does the circumference of darkness surrounding it." --Albert Einstein -------------------- Posts: 536 | Registered: Sunday, September 7 2003 07:00 |
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Guardian
Member # 6670
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written Monday, April 10 2006 09:04
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I was about to disagree with you, but then I when over my method again. Oops. Got it now: THE TRICK THE TRICK CON'T I used to have a book full of brainteasers like this. When I get home, I'll look for it. EDIT: Zeviz has most of the solution, look at his post. Mine are even more general hints. -------------------- IF I EVER BECOME AN EVIL OVERLORD: No matter how many shorts we have in the system, my guards will be instructed to treat every surveillance camera malfunction as a full-scale emergency. [ Monday, April 10, 2006 09:06: Message edited by: Dintiradan ] Posts: 1509 | Registered: Tuesday, January 10 2006 08:00 |
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? Man, ? Amazing
Member # 5755
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written Monday, April 10 2006 09:24
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quote:As correctly answered by Slarty, the two words combined have 11 letters. -------------------- quote: Posts: 4114 | Registered: Monday, April 25 2005 07:00 |
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Nuke and Pave
Member # 24
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written Monday, April 10 2006 09:39
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I've just noticed that the question was about 12 pills, rather than 9. I guess I should have read it more carefully. My intended solution no longer works, although my hints are general enough that they might still apply. The best solution I have at the moment has 1/6 chance of failure. (You might end up with 2 pills you haven't sorted after 3 measurements if you are unlucky.) EDIT: I figured out the solution and it turns out that my original hints still apply with following modifications: Hint 1 has different interpretations for first weighting and second weighting. Hint 2 applies only to second wighting. Here are more specific hints: hint 3 There are two possible results of first weighting. Next three hints apply to harder case. For easy case, consider my old hint 2. hint 4 hint 5 hint 6 [ Monday, April 10, 2006 10:20: Message edited by: Zeviz ] -------------------- Be careful with a word, as you would with a sword, For it too has the power to kill. However well placed word, unlike a well placed sword, Can also have the power to heal. Posts: 2649 | Registered: Wednesday, October 3 2001 07:00 |
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Agent
Member # 5814
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written Monday, April 10 2006 15:55
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quote:It seems as if everyone caught on anyway, but I just want to clarify because the mistake was mine:  -------------------- quote: Posts: 1115 | Registered: Sunday, May 15 2005 07:00 |
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Shaper
Member # 247
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written Tuesday, April 11 2006 14:13
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Ah, brain teasers. If only I had the logic, or lack of, to follow one through. -------------------- The Knight Between Posts. Posts: 2395 | Registered: Friday, November 2 2001 08:00 |
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Law Bringer
Member # 2984
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written Tuesday, April 11 2006 23:12
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Edit: This entire post is one big spoiler. Scroll down until you see my signature if you don't want to see it. I see Zeviz has apparently solved it completely (without any "unlucky" outcomes), but I'll keep this up: Divide into 4 groups of 3, A,B,C and D. Now, once you know in which of the groups the odd ball is and whether it is lighter or heavier, you can determine which it is with a single additional attempt. Compare A and B. 1. If A<B, compare A and C 1.1 If A=C, the odd one is in B and is heavier. 1.2 If A<C, the odd one is in A and is lighter. 2. If A>B, compare A and C 2.1 If A=C, the odd one is in B and is lighter. 2.2 If A>C, the odd one is in A and is heavier. 3. If A=B, compare A and C. 3.1 If A<C, the odd one is in C and is heavier. 3.2 If A>C, the odd one is in C and is lighter. 3.3 If A=C, the odd one is in D, but you do not know if it is lighter or heavier. You're partly screwed, but you might still find out something, at least. Compare two balls of D. 3.3.1 If the balls are equal, the third ball is the odd one, but you still don't know if it is lighter or heavier. 3.3.2 If the balls are not equal, you're screwed. -------------- With this method, you are sure to narrow down the possibilities to two balls, in the worst case. Since there are 24 possibilities you must check for, your chance of finding out both the ball and its property with this method is 75% (ie, the chance that it is not in D). Your chance of finding the ball is 83.3~% (with 8.3~% probability of not finding out how the ball differs from the rest). Your chance of only narrowing it down to two is 16.6~%. ------------------ I can't think of a way to improve on this strategy, though... [ Tuesday, April 11, 2006 23:18: Message edited by: Kuranes- ] -------------------- Encyclopaedia Ermariana • Forum Archives • Forum Statistics • RSS [Topic / Forum] My Blog • Polaris • I eat novels for breakfast. Polaris is dead, long live Polaris. Look on my works, ye mighty, and despair. Posts: 8752 | Registered: Wednesday, May 14 2003 07:00 |
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Raven v. Writing Desk
Member # 261
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written Wednesday, April 12 2006 04:37
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100% Success Solution (Spoiler) The trick is in maximizing collection and use of information. You need to use groups of different sizes to maximize information collection, and you also need to realize that, in a weighing of two apparently equally likely groups, it is CRITICAL to note which group is heavier or lighter, as this allows you to squeeze more information out of the same future weighings. Because if a pill X is the light side of the scale in one weighing, and the heavy side of the scale in another weighing, you know it cannot be the culprit! I'll label the pills ABCDEFGHIJKL for convenience. For steps, I'll use the following notation: each step gets a number. After the first step, =>< indicates the result leading to another step. So "1=2." would tell you that this is step 2, and you do it iff your step 1 weighing resulted in balanced scales. "1>3>5." Would tell you that this is step 5, and you do it iff step 3 had a heavier left side, which you do iff step 1 had a heavier left side. 1. Weigh ABCD vs EFGH. 1=2. Weigh IJK vs ABC. 1=2=Answer, L 1=2>3. Weigh I vs J. 1=2>3=Answer, K 1=2>3>Answer, I 1=2>3<Answer, J 1>4. Weigh ABE vs CDF. 1>4=5. Weigh G vs H. 1>4=5=...Impossible 1>4=5>Answer, H 1>4=5<Answer, G 1>4>6. Weigh A vs B. 1>4>6=Answer, F 1>4>6>Answer, A 1>4>6<Answer, B 1>4<7. Weigh C vs D. 1>4<7=Answer, E 1>4<7>Answer, C 1>4<7<Answer, D 1<8. Weigh ABE vs CDF. 1<8=9. Weigh G vs H. 1<8=9=...Impossible 1<8=9>Answer, G 1<8=9<Answer, H 1<8>10. Weigh C vs D. 1<8>10=Answer, E 1<8>10>Answer, D 1<8>10<Answer, C 1<8<11. Weigh A vs B. 1<8<11=Answer, F 1<8<11>Answer, B 1<8<11<Answer, A -------------------- Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560 | Registered: Wednesday, November 7 2001 08:00 |
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Nuke and Pave
Member # 24
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written Wednesday, April 12 2006 09:38
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It seems there is more than one right answer. Here is the one I was referring to in my last post. -----------SPOILER------------- Easy case is the same: 1. Weigh ABCD vs EFGH. 2a. If {ABCD=EFGH}, Weigh IJK vs ABC. 3a. IF {IJK=ABC}, Weigh L against anything. 3b. IF {IJK<ABC}, we know that IJK is too light, so weigh I against J. 4a. IF {I=J}, answer is K. 4b. IF {I<J}, answer is I, otherwise J. Step 2 of harder case is different: 2b. IF {ABCD<EFGH}, Weigh ABCE against DIJK. 3c. IF {ABCE=DIJK}, we know that FGH is too heavy, so weigh F against G. 4c. IF {F=G}, H is too heavy. 4d. IF {F>G}, F is too heavy, otherwise G is too heavy. 3d. IF {ABCE<DIJK}, we know that ABC is too light, so weight A against B, etc. 3d. IF {ABCE>DIJK}, we know that either E is too heavy or D is too light, so weigh D against A. 4e. IF {D<A}, D is too light, otherwise E is too heavy. ---------END SPOILER---------- -------------------- Be careful with a word, as you would with a sword, For it too has the power to kill. However well placed word, unlike a well placed sword, Can also have the power to heal. Posts: 2649 | Registered: Wednesday, October 3 2001 07:00 |