Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:21:34 GMT -5
Candy Cane ColleenzMessage #709 - 10/14/10 04:00 PMIs #4 gondoliers? Candy Cane ColleenzMessage #710 - 10/14/10 04:01 PM#4 - remodeling Virgil SyonidMessage #711 - 10/14/10 04:29 PMThe standings thus far:1. BUSTERS (apple +5) 2. RACKET (Tall +6) 3. STRIPED (SBS +8) 4. REMODELING (colleenz +10) 5. SCARLET (SBS +10) 6. STOMPING (apple +10) 7. DECLARES (SBS +13) 8. 9. DILATES (apple +17) 10. ADAPTERS > ADOPTERS (colleenz +25) colleenz: 35 apple: 32 SBS: 31 Tall: 6 One left! Colleenz missed #8 because her suggested "SULFIDE" has an E next to a D. Who will be the winnah? Snow Bunny SpriteMessage #713 - 10/14/10 04:42 PMOne left! Colleenz missed #8 because her suggested "SULFIDE" has an E next to a D.
Does the answer have an extra Canadian u?
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:22:04 GMT -5
Virgil SyonidMessage #714 - 10/14/10 04:50 PM<adds Virgil to "The List> Ms. Wench indicated that you and Mr. Up were an "item" in days of yore. ![](http://boards.msn.com/Themes/default/emoticons/guy_hug.gif) ![](http://boards.msn.com/Themes/default/emoticons/girl_hug.gif) My apologies, ma'am, but his "character" succeeds in creeping me out. Like "Moe" on the Simpsons. Does the answer have an extra Canadian u? Certainly nout. Snow Bunny SpriteMessage #715 - 10/14/10 04:55 PMHmmm, well I give up. I found refiled and fielder, but those both are excluded based on the rules. C'mon Apple and Colleen, save us! beerwench over 29000 bits of drivel postedMessage #716 - 10/14/10 04:56 PMLike "Moe" on the Simpsons. LOL! You too, huh? ![](http://boards.msn.com/Themes/default/emoticons/teeth_smile.gif) Candy Cane ColleenzMessage #717 - 10/14/10 05:03 PMIs it a Canadian spelling of fluoride?
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:22:34 GMT -5
Snow Bunny SpriteMessage #718 - 10/14/10 05:14 PMOh it better NOT be! Virgil, you are in big trouble. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) 973beachbumMessage #719 - 10/14/10 05:20 PM but his "character" succeeds in creeping me out. Like "Moe" on the Simpsons.
So you do know MU. Virgil SyonidMessage #720 - 10/14/10 10:28 PMUhhh.... OK. So I checked my answer for 8, and realized that the 'no E and D' rule for eliminating "DEFILER", "REFILED" and "SULFIDE" also inadvertently eliminated "FIELDER", which was the "correct" answer. ![](http://boards.msn.com/Themes/default/emoticons/red_smile.gif) Instead, the tie-breaker question is renominated as follows: INADVERTENT > _ _ _ _ _ _ _ _ _ _ _ > RENOMINATED I deem it worth 30 points so that Tall has a shot at a win. ![](http://boards.msn.com/Themes/default/emoticons/wink_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:23:26 GMT -5
rovoMessage #721 - 10/14/10 10:33 PMOh yeah. Rigging the game will surely make the posters happy. ![](http://boards.msn.com/Themes/default/emoticons/what_smile.gif) --appleMessage #722 - 10/14/10 10:35 PMDETERMINANT ![](http://boards.msn.com/Themes/default/emoticons/teeth_smile.gif) Snow Bunny SpriteMessage #723 - 10/14/10 10:35 PM![](http://boards.msn.com/Themes/default/emoticons/sad_smile.gif) Yup, rovo's right. I'm not playing this teaser anymore. Virgil gets -5000 points. 973beachbumMessage #724 - 10/14/10 10:37 PMYup, rovo's right. I'm not playing this teaser anymore. Virgil gets -5000 points. Ahhhh come on. Virgil is only showing off his warm and fuzzy side. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:23:56 GMT -5
--appleMessage #725 - 10/14/10 10:38 PMI was also stuck on the last one, I came up with Sulfide--I would have put it but I play by the rules ![](http://boards.msn.com/Themes/default/emoticons/angel_smile.gif) Snow Bunny SpriteMessage #726 - 10/14/10 10:39 PMVirgil is only showing off his warm and fuzzy side. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Those are his wolfskin shoes that you see. --appleMessage #727 - 10/14/10 10:39 PMWell, I'll still crush on Virgil, after all, my name is in the title! Snow Bunny SpriteMessage #728 - 10/14/10 10:40 PMI play by the rules ![](http://boards.msn.com/Themes/default/emoticons/angel_smile.gif) <<Tea all over the monitor>> ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:24:26 GMT -5
Snow Bunny SpriteMessage #729 - 10/14/10 10:42 PMWell, I'll still crush on Virgil, Well I do too, but Virgil is still changing rules at the last minute and should be racked over the coals. Besides, rovo is my bigger crush, so he must be right. 973beachbumMessage #730 - 10/14/10 10:43 PMYou gotta love someone with big enough .... to put an ![](http://boards.msn.com/Themes/default/emoticons/angel_smile.gif) after her comment with the name little apple tart.![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) --appleMessage #731 - 10/14/10 10:48 PMYou like? Empire SB helped me come up with it You know, sugar and spice and everything nice, but still just a little tart. Virgil SyonidMessage #732 - 10/14/10 11:46 PMA few twists and turns (that are no fault of Virgil's ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) ) yields the contest winner!: 1. BUSTERS (apple +5) 2. RACKET (Tall +6) 3. STRIPED (SBS +8) 4. REMODELING (colleenz +10) 5. SCARLET (SBS +10) 6. STOMPING (apple +10) 7. DECLARES (SBS +13) 8. DETERMINANT (apple +tiebreak) 9. DILATES (apple +17) 10. ADAPTERS > ADOPTERS (colleenz +25) apple: 32 + tiebreak ![](http://boards.msn.com/Themes/default/emoticons/star.gif) colleenz: 35 SBS: 31 Tall: 6 Apologies for "changing the rules". A tie-breaker question seemed like the only fair way to rectify the situation. As for its 30-point value, the problem's potential influence on the standings is identical to the original 13-point problem, with the sole exception that good Tall and true had a chance of winning the game. Hence, your cruel words have lashed me for the kindness I extended to one of EE's most beloved moderators. ![](http://boards.msn.com/Themes/default/emoticons/cry_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:25:17 GMT -5
Snow Bunny SpriteMessage #733 - 10/15/10 12:12 AMHmmmm, I don't see the -5000 points for Virgil on the list. A tie-breaker question seemed like the only fair way to rectify the situation. Yabbut, I was WORKING at the time you posted it and then I was too busy whining about how unfair the world was after I spent like HOURS of EE-standard time (10 minutes IRL-time) earlier on trying to come up with a solution and my tears of frustration caused my co-workers to agonize over my predicament. And now, I'm working late because I couldn't get my real work done on time. All in all, a truly miserable day. Ok, I'm done (and the above may be just a slight exaggeration). ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Virgil SyonidMessage #734 - 10/15/10 12:31 AMHOURS of EE-standard time (10 minutes IRL-time) Time dilation! It all seems to so obvious now! I suspected something supernatural when M. Margarita claimed clicking on links was "too hard". Snow Bunny SpriteMessage #735 - 10/15/10 12:54 AM![](http://boards.msn.com/Themes/default/emoticons/what_smile.gif) Why else would we need lots of easy-to-access emoticons? Or we get easily dis... ohhhh, shiny! Virgil SyonidMessage #736 - 10/15/10 01:04 AMActually, it was a must-read article on why [ b.rox.com/2008/10/31/why-halloween-sucks/] Halloween sucks. ![](http://boards.msn.com/Themes/default/emoticons/wink_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:25:48 GMT -5
Snow Bunny SpriteMessage #737 - 10/15/10 02:37 AMIt's kinda cute that you think EEers click on links. --------------------------------------------------------------------- BTW, I did read it and I too detest the materialism of the holidays - any holiday. I still like wearing a cyber-costume though. ![](http://boards.msn.com/Themes/default/emoticons/teeth_smile.gif) Virgil SyonidMessage #738 - 10/15/10 06:51 AMProblem 52 - The Tortoise and the HareThe tortoise and the hare are having a race. The hare runs several times faster than the tortoise, and so he gives the tortoise a head start. Now, let A be the location of the tortoise when the hare starts to run. By the time the hare reaches A, the tortoise will have moved forward. He will therefore be at point B, which is ahead of point A. By the time the hare reaches point B, the tortoise will have moved forward to point C, which is ahead of point B. Obviously, as this continues to happen, the tortoise will always have moved ahead by the time the hare reaches his previous position. Hence, we must conclude that the tortoise is always in the lead and is guaranteed to win the race. Or is my logic faulty? And if so, how? --appleMessage #739 - 10/15/10 07:15 AMETA: fixed my time/distance mix-up (maybe I was all alone so nobody noticed anyway?) Virgil, it is way past my bedtime, but I am so logic based, math, physics and all that. And yes, the logic is flawed, because at some point a fast speed (delta hare-distance/delta time) will be able to overtake a slow speed (tortoise head-start + delta tortoise-distance/delta time). But I'm tired, and feel like pointing out the obvious would be like trying to explain things to a democrat You could set the distance for a point way out there, and not change it for the equation. So your two "divided into" numbers of time (don't laugh at me, I've been up for 20+ hours and can't think of the correct terms ETA: denominator) would be the same on both equations. But the delta hare-distance would be much greater then the delta-tortoise-distance, even adding that head start. If your delta-hare Numerator is large enough, and the denominator small enough, mathematically the tortoise won't stand a chance. Oh, could we change tortoise to ![](http://boards.msn.com/Themes/default/emoticons/53_53.gif) and hare to ![](http://boards.msn.com/Themes/default/emoticons/dog.gif) ? Maybe pictures will help... But basically, the tortoise will always hit the destination before the hare does, until he gets blown by by the hare. Damn the math nerd in me, I will be forced to come up with numbers ![](http://boards.msn.com/Themes/default/emoticons/48_48.gif) --appleMessage #740 - 10/15/10 07:31 AMLets say that the race is 50 miles long, the tortoise gets a 20 mile head start (2 hours). The tortoise goes 10 miles/hour (yes, we're doing English measurements) and the hare goes 100 miles/hour. Two hours into the race the tortoise is at the 20 mile marker, and the hare takes off. Three hours into the race, the tortoise has reached the 30 mile marker (20 miles +10 miles/1 hour) but the hare, running 100 miles an hour, crossed the finish line half an hour ago (50 miles at 100 miles/1 hour is half an hour). The tortoise is no longer ahead of the hare, so he must have lost the lead. Thus proving that words really mean nothing in the end, and just cuz it sounds good doesn't make it so ![](http://boards.msn.com/Themes/default/emoticons/teeth_smile.gif) . (or, verbal logic is flawed, math logic is better) I'm going to bed now ![](http://boards.msn.com/Themes/default/emoticons/77_77.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:26:18 GMT -5
Virgil SyonidMessage #741 - 10/15/10 07:51 AMThree hours into the race, the tortoise has reached the 30 mile marker (20 miles +10 miles/1 hour) but the hare, running 100 miles an hour, crossed the finish line half an hour ago (50 miles at 100 miles/1 hour is half an hour). The tortoise is no longer ahead of the hare, so he must have lost the lead. Hmm. It would appear that way. But we have a concrete proof in #738 that the hare never catches the tortoise. Hence, we must conclude that the hare can only run 16.6 miles/hour, which is the speed at which the hare just about catches the tortoise but doesn't violate our proven law of "tortoise is always ahead". And if you think about it, 16.6 miles/hour sustained sprint for a hare is very reasonable. A 100-mph hare is a physical impossibility. And now you've proven that a hare faster than 16.6 mph is also a mathematical impossibility. So credit for the problem goes to apple. ![](http://boards.msn.com/Themes/default/emoticons/thumbs_up.gif) Candy Cane ColleenzMessage #742 - 10/15/10 12:04 PMrectify the situation Better not let SJ hear you talk like that ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) beerwench over 29000 bits of drivel postedMessage #743 - 10/15/10 12:37 PMLOL! And everyone knows that the hare is going to need a nap at some point, so he won't win anyway. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Snow Bunny SpriteMessage #744 - 10/15/10 02:05 PMwe have a concrete proof in #738 that the hare never catches the tortoise ![](http://boards.msn.com/Themes/default/emoticons/what_smile.gif) What did you do to the poor lil' bunny? Are you part of the Canadian mafia? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:27:09 GMT -5
--appleMessage #745 - 10/15/10 02:31 PMwe have a concrete proof in #738 that the hare never catches the tortoise You know, they said that about Wile E. Coyote and the road runner too, but he did! [ ] (it's not the family guy one, and if you don't like links look up Coyote catches road runner on youtube) Snow Bunny SpriteMessage #746 - 10/15/10 02:37 PMLOL! Here's one where Elmer Fudd is the Canadian mountie. Poor Bugs. [ ] --appleMessage #747 - 10/15/10 03:24 PMI remember that one from when I was little. Notice the graffiti on the wanted poster makes him look like Hitler? I didn't catch all the WWII references then, but they're easy to spot now. GameshowMessage #748 - 10/15/10 03:52 PMThis reminds me of the "arrow" scenario. If you shoot an arrow at someone, what is the time for the arrow to travel half the distance to the target. Then, what is the time for the arrow to travel half of the remaining half of the distance? (rinse and repeat, rinse and repeat). Technically, there are an "infinite" halving of the distance between the arrow and target. So will the arrow ever reach the target? Hmmm, looking back, I think I may have confused myself more by writing that, so I'll take a stab at the answer. Yes, the Hare will eventually overtake the tortoise. Because eventually, the distance between the two becomes infinitely short that the hare will "catch up" and then pass the tortoise. The distance itself is irrelevant. Rather, the time it takes to cover that distance becomes too short to matter (At a certain point, the distance between the hare and tortoise will be less than a second. So in a 1 second span, the hare will pass the tortoise). anyways, my 2 cents -Ben
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:27:39 GMT -5
Dr. PigMessage #749 - 10/15/10 04:04 PMThat's just Zeno's paradox. Holds true for infinite or non converging sums but not finite or converging ones. And the race distance is certainly a finite sum. Snow Bunny SpriteMessage #750 - 10/15/10 04:06 PMOh, were we supposed to still solve the problem? ![](http://boards.msn.com/Themes/default/emoticons/confused_smile.gif) I thought Virgil already gave Apple credit. Virgil SyonidMessage #751 - 10/15/10 04:35 PMActually, Dr. Pig's explanation about the Zeno effect in #749 is the correct answer. The series of distances traveled by the tortoise until the hare catches up, {A-0, B-A, C-B, D-C, ...}, is geometric and Cauchy. It therefore has a sum that converges absolutely to a limit, K, where K is the distance that the hare overtakes the tortoise. After this point, the terms in the series flip sign and become divergent. I thought Virgil already gave Apple credit. OK. I realize I didn't put in any goofy faces. But you seriously think my spiel about a mathematically-defined maximum hare speed wasn't just a bit satirical? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Snow Bunny SpriteMessage #752 - 10/15/10 04:57 PMBut you seriously think my spiel about a mathematically-defined maximum hare speed wasn't just a bit satirical? Do you seriously think I actually tried to comprehend either of your's or Apple's posts? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:28:09 GMT -5
--appleMessage #753 - 10/15/10 05:25 PMI was just pointing out that words and philosophical "logic" are screwy and math is better... I understand I get credit for the math part, but Virgil did say that there was "concrete proof" that wasn't the case, so the Zeno effect still could be mentioned for intended credit. Can I still crush on Virgil? I do know that an organism that doubles in size every second can take an hour to fill up a container but only takes one more second to fill it. Snow Bunny SpriteMessage #754 - 10/15/10 06:25 PMwords and philosophical "logic" are screwy and math is better... Math seems pretty screwy too. Can I still crush Virgil? fixed. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) --appleMessage #755 - 10/15/10 07:01 PM
Math seems pretty screwy too. Only when you get into the imaginary parts, then it gets really fun. Virgil SyonidMessage #756 - 10/15/10 07:55 PMOK. Here's an odd mathy question for all of you. Consider the number x = 0.999999.... with an infinite number of 9's. Which of the following statements is true?:
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:29:01 GMT -5
Snow Bunny SpriteMessage #757 - 10/15/10 08:04 PM![](http://boards.msn.com/Themes/default/emoticons/72_72.gif) Is that a trick question? Well, it is from Virgil, so yes. Thus it's not 1. ![](http://boards.msn.com/Themes/default/emoticons/lightbulb.gif) I'm going with: 1x < 1 AND 3x > 1. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Candy Cane ColleenzMessage #758 - 10/15/10 08:10 PMI am going with #1, but my head hurts. I am filling out KINDERGARTEN applications for next year - you would not believe what they ask for. --appleMessage #759 - 10/15/10 08:42 PMI ![](http://boards.msn.com/Themes/default/emoticons/heart.gif) crazy math. So, #1 is true, because obviously .9 to infinity will never equal 1 (like Zeno effect) BUT, 1/3= .3 to infinity, and we all know that .3 to infinity equals .9 to infinity, but since 1/3 x 3 = 1, then .9 to infinity must also equal 1 I haven't figured out how to prove #3 yet. Love math but I'm rusty. But, "close enough for government work," right? GameshowMessage #760 - 10/15/10 10:53 PMx=1 1/9 = .111111(infinite 1's) so .1111111*9 = .99999(infinite 9's) 1/9 * 9 = 9/9 = 1 Or another way to look at it. if x = .999999 (infinite 9's) Then 10x = 9.999999 (infinite 9's) 10x - x = 9 (since all the infinite 9's delete each other out) 9x = 9 x = 1 My 2 cents -Ben
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Virgil Showlion
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Post by Virgil Showlion on Dec 23, 2010 2:29:31 GMT -5
Virgil SyonidMessage #761 - 10/15/10 11:03 PMGameshow got it in #760. The answer is b) x = 1. Most people would intuitively say that 0.9999.... is ever-so-slightly less than 1. But as Gameshow's second proof elegantly points out, the two numbers are identical in the real number system. (Note that certain obscure number systems exist where x /= 1, but they have awkward cyclic properties, etc.) Candy Cane ColleenzMessage #763 - 10/16/10 10:41 PMCan I still crush on Virgil? Sure! Since Velma dropped Shaggy you can have Virgil and I'll take Scooby. Wanna double date for Pizza ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Virgil SyonidMessage #764 - 10/16/10 11:07 PMProblem 53 - All Stacked UpYou live in a world called "Flatland". In Flatland, the ground everywhere is perfectly flat. Quarters in flatland are perfectly flat cylinders with a radius of 1" and thickness of 0.1". You and a friend are having a competition to build "towers" by stacking up Flatland quarters one on top of another. However, the goal is not to build the highest coin tower, but instead the tower that leans the most. That is, if you dropped a string straight down from the center of the top coin to a point A on the ground, the distance between A and the center of the bottom coin is the amount the tower "leans". What is the greatest distance a tower can lean before falling over, and how is the tower constructed? (Note, the quarters must be stacked one on top of another face to face. There is no glue, etc. You have an unlimited number of quarters.) ALLOWED NOT ALLOWED [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ----------------------------------------------------------------- Scottish_SugarPlumMessage #765 - 10/17/10 03:38 AM(Note, the quarters must be stacked one on top of another face to face Since the quarters must be stacked face-to-face, the tower could only be two quarters high. Therefore the quarters would be stacked like this and therefore wouldn't fall over. [ ] (face-down) [ ] (face-up) ------------------
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Post by Virgil Showlion on Dec 23, 2010 2:30:01 GMT -5
rovoMessage #766 - 10/17/10 04:14 AMhow is the tower constructed We could weld the quarters together. clannish, His example shows 4 stacked. Is he trying to misguide us into breaking the face-to-face rule? --appleMessage #767 - 10/17/10 05:16 AMMaybe it's a Canadian thing...I know the nickel had a beaver on it so I guess technically that had two faces ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Assuming "face" means any side of a coin that looks like a circle, with a radius of 1" you'd have a diameter of 2". I know you could stack them so that just the edge of one coin could be balanced under the weight of several more coins. But you'd still have to catch that edge. So my thought is that you can get the coins to "lean" a distance of 1.9" center to center. --appleMessage #768 - 10/17/10 05:19 AMLike this [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
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Post by Virgil Showlion on Dec 23, 2010 2:30:53 GMT -5
Virgil SyonidMessage #769 - 10/17/10 08:15 AM"Face to face" means "flat side to flat side". That is, no stacking coins end to end. Besides, if the coins are perfect cylinders, it means that neither side is embossed or recessed with a head/tails relief. Consider them "ideal" cylinders. ![](http://boards.msn.com/Themes/default/emoticons/wink_smile.gif) And unfortunately, apple, your configuration in #768 is unstable even if the sixth coin could be "pinched" as shown. The stack will topple over to the right. However... as the stack on top of the sixth coin grows to infinite height, the 'offset' needed to make the tower stable goes to zero. In this modified version of your solution, you get a distance of ~2". Even though the coin with the highest offset isn't the top coin, you get credit for a 2" solution. So the challenge to the rest of you is to build a stable coin stack that beats apple's "lean" of 2". ![](http://boards.msn.com/Themes/default/emoticons/shades_smile.gif) GameshowMessage #770 - 10/21/10 05:07 PMI figure you only need two Quarters (stacks) First Quarter is on the bottom. Second quarter is the furthest you can place it without it leaning over (49.99999%) If I recall, you must take the "top coin", so wedging a coin further than 50% is no good because you have to use the coin on top. Anyways, that's my theory -Ben Virgil SyonidMessage #771 - 11/02/10 05:30 AM(Solution to Problem 53) --apple wins "best attempt" prize with her solution of 2". The actual solution, believe it or not, is that you can get a stack of perfectly flat coins to lean by any amount in any direction. How you accomplish this is a bit tricky (the proof involves some mathematical arguments that I doubt many EEers would be interested in). Suffice it to say that the amount you can "lean" a tower is proportional to the logarithm of the height of the tower. Hence, if you can lean a tower of 2 coins over by 1 inch and a tower of 10 coins over by 2 inches, getting the tower to lean 3 inches would take 50 coins, getting it to lean 4 inches would take 250 coins, and getting it to lean over 10 inches would take 3,906,250 coins! ![](http://boards.msn.com/Themes/default/emoticons/omg_smile.gif) Virgil SyonidMessage #772 - 11/02/10 05:33 AMProblem 54 - Another Foolproof Get-Rich-Quick SchemeProblem 54 is a two-parter, with an easy part and a hard part. Those who attempt the hard part (which is more mathematical) should leave the easy part to less mathematically-inclined EEers. EASYThe following prospectus was posted by Mr. Willis B. Powell on the Associated Press newswire in 1875: "Glorious Opportunity To Get Rich!!! · We are starting a cat ranch in Lacon with 100,000 cats. Each cat will average 12 kittens a year. The cat skins will sell for 30 cents each. One hundred men can skin 5,000 cats a day. We figure a daily net profit of over $10,000. Now what shall we feed the cats? We will start a rat farm next door with 1,000,000 rats. The rats breed 12 times faster than the cats. So we will have four rats to feed each day to each cat. Now what shall we feed the rats? We will feed the rats the carcasses of the cats after they have been skinned. Now Get This! We feed the rats to the cats and the cats to the rats and get the cat skins for nothing!" It is a matter of historical record that several dozen men showed up at the Associated Press office to inquire about the prospectus. All were turned away for the position of "cat skinner" (and were rather furious that they had been turned down). Based on only the information in the prospectus itself, explain why. HARDSuppose you're a rich, well-respected gentleman/lady with a good rapport at a casino that has generously given you an unlimited line of credit. Your favourite game is roulette, and you play on the standard American wheel that gives you close to a 50%/50% chance on doubling/losing your money when you play red/black. Your gambling strategy is this: - You start with $0 in pocket.
- You place a bet of $1. If you don't have the $1 in pocket, you simply borrow a dollar from your LOC.
- If the ball lands on red (roughtly 50% chance), you win and you get double your bet back (in this case, $2). You pocket your winnings and go back to step 2 to play again.
- If the ball lands on black, your bet is lost. But rather than "give up", you double up on your next bet. So if you just lost $1, you bet $2. If you just lost $2, you bet $4, etc.
- You continue doubling up your bet as long as you lose. Eventually the ball will hit red and you'll win back all the money you've lost so far plus an additional dollar. For example, if you lose $1, $2, $4, and then $8 dollars in a row (a nasty unlucky streak) you will recoup your $15 loss plus $1 by hitting red on your $16 dollar bet. If you get another black, you'll recoup your $31 loss plus $1 by hitting red on your $32 bet. (It's statistically inevitable that the unlucky streak will end sometime.)
If any any time your pocket money goes to zero, you simply borrow the remainder of the bet from your LOC.
- After a recouping your losses plus one dollar after a streak of blacks, your bet goes back to $1 and you go back to step 2.
So no matter what happens: a red, or a streak of blacks followed by a red, you always end up with one dollar more at the end of each gambit. Naturally, you can earn a cool hundred dollars by playing a hundred gambits. You've discovered the perfect way to get rich quick! Or have you? (And for you skeptics: why not?) ![](http://boards.msn.com/Themes/default/emoticons/71_71.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:31:23 GMT -5
Virgil SyonidMessage #773 - 11/02/10 05:34 AMIncidentally, apologies for the rare updates to the thread lately, but I've run out of brainteasers in my main archives. I'll post new and interesting brainteasers as I come across them. Candy Cane ColleenzMessage #774 - 11/02/10 12:27 PMWoo Hoo - Where is this casino with no table limits? Virgil SyonidMessage #775 - 11/02/10 04:56 PMWoo Hoo - Where is this casino with no table limits? Ehm. I'll tell you after you've popped a few Thorazine. ![](http://boards.msn.com/Themes/default/emoticons/what_smile.gif) Come on, people! Nobody except turkey junkies for this preemo batch of brainteasers? SlowbutSureMessage #776 - 11/02/10 05:06 PMCome on, people! Working, Virgil, working... ![](http://boards.msn.com/Themes/default/emoticons/sad_smile.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:31:53 GMT -5
SlowbutSureMessage #777 - 11/02/10 05:41 PM(And for you skeptics: why not?) Although I've temporarily "won" since I do end up with one dollar more at the end of each gambit, I still have to pay back my LOC. ![](http://boards.msn.com/Themes/default/emoticons/sad_smile.gif) The casino won't let me win anything, will it? It's making me double-up on my loses, but I can only win $1 at a time. GameshowMessage #778 - 11/02/10 05:51 PMHard one: I think that's the Martingale methodology. Unfortunately, the plan doesn't work because a person typically has a finite amount to lose and when they hit it, they have nothing left to wager with. In this scenario, the person has an infinite line of credit. So even if a million, billion, trillion, heck a google of blacks come up in a row, the person will still have the line of credit to make the next wager (even though that number will be incredibly large). However, you have the person starting with their own money first and only dipping into the credit line when they have no more money in their pocket. So, in a way, although they can't lose, they aren't going to win because they have to utilize their winnings first. Now, if you say they pocket all winnings and use their Line of credit everytime they play, then they would eek out a profit ($1 at a time). My 2 cents -ben Virgil SyonidMessage #779 - 11/02/10 07:05 PMBen, you're very close to being "right on the money", so to speak. In this case, the problem is that for any finite LOC, the gambler's wealth is a supermartingale. Your large chances of winning cash in $1 increments is wiped out (and in fact reduced, because of the slight wheel bias) by a small probability of your LOC being exhausted. I believe the expression is "picking up nickels in front of a steamroller". However, with an infinite LOC as given in the problem, the wealth stochastic process (e.g. W(1),W(2),...,W(n)) is no longer an integrable series (it isn't bounded) and ceases to be a supermartingale. A quick analysis reveals that, although your cashflow will go negative an infinite number of times, given any positive wealth, W0, the expected value of the time needed to attain a wealth W1 > W0 is finite for all W0. Hence, there is no upper limit to the series and for any finite dollar amount M that you wish "win", your wealth W --> Wn > M in finite time a.s. Naturally, in real life this latter case is impossible since there's no such thing as an infinite line of credit. Candy Cane ColleenzMessage #780 - 11/02/10 08:11 PMNaturally, in real life this latter case is impossible since there's no such thing as an infinite line of credit.
Could someone tell that to Obama?
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Post by Virgil Showlion on Dec 23, 2010 2:32:44 GMT -5
unrepentant spendthriftMessage #781 - 11/02/10 10:02 PMCould someone tell that to Obama You get your chance today, Colleenz. Vote!! I can't believe I'm striggling with the easy part, I must be tired. Will look at it again tommorow.......... Virgil SyonidMessage #782 - 11/09/10 12:41 AM(Solution to Problem 54)Gameshow gives the correct answer to the HARD problem in #778, followed by some additional explanation in #779. I'm leaving the EASY part of problem 54 open to all parties now. Virgil SyonidMessage #783 - 11/09/10 12:42 AMProblem 55 - Gone to the DogsOne of the furrier problems from [ www.collegepuzzlechallenge.com/Archive/2010/] Microsoft's 2010 College Puzzle Challenge. Combine pictures to form the names of breeds of dogs. They may be horizontal, vertical, forwards, or backwards, but they always occur in a straight line. A picture may be reused, but only has one correct interpretation. Read the leftover pictures top to bottom to form your thematic answer. ![](http://img837.imageshack.us/img837/927/gonetothedogs.jpg) rovoMessage #784 - 11/09/10 01:01 AMI don't know. Like D1 + D4 = D3 ![???](//storage.proboards.com/forum/images/smiley/huh.png) ? ![](http://boards.msn.com/Themes/default/emoticons/confused_smile.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:33:14 GMT -5
beerwench over 29000 bits of drivel posted Message #785 - 11/09/10 01:16 AM
Like A4 + A5 = Corgi
beerwench over 29000 bits of drivel posted Message #786 - 11/09/10 01:17 AM
D5 + E5 = Shitzu
beerwench over 29000 bits of drivel posted Message #787 - 11/09/10 01:18 AM
F2 + 3 + 4 = Pekinese
Kansas Beachbum Message #788 - 11/09/10 01:19 AM
Some of my spelling is off, but here goes: A1 - A2 = Beagle. A1 - C1 = Bichon Friese. C4 - F4 = Great Pyranesse. F2 - F4 = Pekenese. C5 - B5 = Mastiff. D5 - E5 - Shitzoo. That's all I got...
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Post by Virgil Showlion on Dec 23, 2010 2:33:45 GMT -5
beerwench over 29000 bits of drivel postedMessage #789 - 11/09/10 01:19 AM1A + B + C + D = Bichon Frise Virgil SyonidMessage #790 - 11/09/10 01:35 AMAll right so far. The goal of the puzzle is to have only one square left over per row. Then those sound out the answer. ![](http://boards.msn.com/Themes/default/emoticons/thumbs_up.gif) LongSamMessage #791 - 11/09/10 01:37 AM<you know, Virgil is really trying to wipe all of you out by over exerting your brains> IHearYou2Message #792 - 11/09/10 01:38 AMD2+E2=DINGO that's the easiest one there, what the hell is wrong with people. ![](http://boards.msn.com/Themes/default/emoticons/angry_smile.gif) I'm not helping anymore! ![](http://boards.msn.com/Themes/default/emoticons/angry_smile.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:34:36 GMT -5
Virgil SyonidMessage #793 - 11/09/10 01:40 AM<you know, Virgil is really trying to wipe all of you out by over exerting your brains> This was considered the easiest puzzle out of the full 27 in the 2010 CPC (link in the problem statement). The winning team (four members) solved all 27 puzzles in just under four hours. So no complainin'! ![](http://boards.msn.com/Themes/default/emoticons/48_48.gif) IHearYou2Message #794 - 11/09/10 01:41 AMHA I just figured out the toughest dog, but I ain't sharing until tomorrow at 9 PST if you ninnies can't figure it out, I'll share my genius with you. Virgil SyonidMessage #795 - 11/09/10 01:46 AMI'll share my genius with you Does your genius include clicking on the link in the problem statement where the answers are posted? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) JennysBeenAGoodGirlMessage #796 - 11/09/10 01:48 AM<you know, Virgil is really trying to wipe all of you out by over exerting your brains> I know, that's why I'm not participating. ![](http://boards.msn.com/Themes/default/emoticons/shades_smile.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:35:06 GMT -5
IHearYou2Message #797 - 11/09/10 01:49 AMinclude clicking on the link in the problem statement where the answers are posted? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
That's a good thought, can I get the answers that way?! Shame on you Virgil for impugning my honor, that is utterly despicable, disgraceful, and repulsive. You've been drinking the fluorated water again haven't you! Virgil SyonidMessage #798 - 11/09/10 02:02 AMShame on you Virgil for impugning my honor I was looking at the IHearYou2 equivalent of "na-na na-na boo boo". What was I supposed to do? ![](http://boards.msn.com/Themes/default/emoticons/angel_smile.gif) MN-InvestorMessage #799 - 11/09/10 02:12 AMC3+D3+E3 = Labrador (LAB + BRA + DOOR) MN-InvestorMessage #800 - 11/09/10 02:28 AMIs B3 + B2 + B1 Dalmation? I don't know what B2 is.
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Post by Virgil Showlion on Dec 23, 2010 2:35:36 GMT -5
Virgil SyonidMessage #801 - 11/09/10 02:37 AMIs B3 + B2 + B1 Dalmation? Yes. B2 is Mae, as in [ space.about.com/cs/formerastronauts/a/jemisonbio.htm] Mae Jemison. Scotch_Laced - MinceTartMessage #802 - 11/09/10 03:12 AMA1-B1 Bichon [Bee Sean] D5-E5 Shih-Tzu [sheet zoo] C5-B5 Mastiff A2-B2 Gull Terr C3-D3-E-3 Labrador A1-A2 Beagle [to be continued.......not done yet] D4-E4-F4 Pyrenese G5-G4-G3-G2 Bearded Collie F2-F3-F4 Pekingese [pea, ken, knees] C1-D1 Shar-Pei [sharp A] G1-G2 Spitz (?) E2-C2-B2 Goberian [Go Berry Anne] Leftover squares : Great Pyredane? (grate, pi, red, N) tall_guyMessage #803 - 11/09/10 06:33 AMThe goal of the puzzle is to have only one square left over per row. Then those sound out the answer. ![](http://boards.msn.com/Themes/default/emoticons/thumbs_up.gif)
Why am I hoping the answer ends up being, "Cats are better?" ![](http://boards.msn.com/Themes/default/emoticons/teeth_smile.gif) Candy Cane ColleenzMessage #804 - 11/09/10 01:19 PME1-F1 - Maltese
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Post by Virgil Showlion on Dec 23, 2010 2:36:28 GMT -5
beerwench over 29000 bits of drivel postedMessage #805 - 11/09/10 01:40 PMGood for you colleenz! I figured that one out on the ride to work today!! I spent last night trying to figure out what dog has "Sith" or "Darth" in it, then did a *facesmack* when I realilzed that it was looking for "Maul". ![](http://boards.msn.com/Themes/default/emoticons/red_smile.gif) Candy Cane ColleenzMessage #806 - 11/09/10 02:34 PMThanks Beer - my 4yo is obsessed with all things Star Wars so I get sucked into it. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) Virgil SyonidMessage #807 - 11/09/10 04:49 PMI think all but one of the breeds has been found so far. Remember, "solving" the puzzle involves using the remaining four squares to sound out an answer. ![](http://boards.msn.com/Themes/default/emoticons/wink_smile.gif) IHearYou2Message #808 - 11/09/10 04:51 PMVirgil they are so damn sloow, this group man oh man. They don't even go for the solution instead creating brand new dog types like Gull Terr, what's happened to our education system?
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Post by Virgil Showlion on Dec 23, 2010 2:36:58 GMT -5
Scotch_Laced - MinceTartMessage #809 - 11/09/10 05:11 PMThey don't even go for the solution instead creating brand new dog types like Gull Terr My solution's not made up. This is a Gull Terr-------> ![](http://media1.picsearch.com/is?Sfv8MHsr2L4BTJ9-igB4A2uwynCDUXGY9Znd04Iw6WQ) Virgil SyonidMessage #810 - 11/09/10 05:56 PMThey don't even go for the solution instead creating brand new dog types like Gull Terr I had to look up "Goberian" and "Great Pyredane" too, IHOP, but they're both breeds. Lassie has a fearsome knowledge of the unnatural things people call mixed breeds. ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif) All of the breeds in the puzzle are pure breeds. Bichon Frise (beachbum) Mastiff (beachbum) Beagle (beachbum) Great Pyrenees (beachbum) Dingo (IHearYou2) Labrador (MN-Investor) Dalmation (MN-Investor) Bearded Collie (Scottish Lassie) Maltese (collenz) Shih-Tzu (beerwench) Corgi (beerwench) Pekingese (beerwench) The squares left over are 1G-2C-3A-4B-5F. IHearYou2Message #811 - 11/09/10 06:45 PMMy solution's not made up. This is a Gull Terr Where's a Terr, I don't see terr in the picture, a terr come on, woman get a grip. Am I supposed to give the answer yet, sigh... Candy Cane ColleenzMessage #812 - 11/09/10 07:08 PMI guessed the final answer when one of the obvious pictures did not line up with others to make the breed name. I am a big fan of this breed though, and currently own a very close breed. Thank goodness for my Dyson.
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Post by Virgil Showlion on Dec 23, 2010 2:37:28 GMT -5
beerwench over 29000 bits of drivel postedMessage #813 - 11/09/10 07:11 PMSiberian Huskey? (thanks for saving it for me everyone ![](http://boards.msn.com/Themes/default/emoticons/49_49.gif) ) IHearYou2Message #814 - 11/09/10 07:22 PMYay we got a winner and it's a huskie, next! Candy Cane ColleenzMessage #815 - 11/09/10 07:44 PMSiberian Huskey WTG Beer! Virgil SyonidMessage #816 - 12/10/10 04:27 AMProblem 56 - EEers on a PlankAs we all know, EEers are an autonomous lot. If you place an EEer on the ground, s/he will walk straight ahead in search of a beer and/or shoe store. All EEers move at the same speed: one mile per hour. Suppose you have five EEers walking left and right along a narrow plank 1 mile long. The plank is only wide enough for one EEer. When two ambling EEers meet each other on the plank, they both reverse direction and head back the way they came. Assume that EEers can complete the turnaround instantaneously. Also assume that the width (front-to-back) of each EEer is negligible. You want to choose the initial position and direction of all five EEers so that at least one of them stays on the plank for the longest possible time. ________________________________________ PoE: "The Loyal Denizen"; targeted; T-16 User: "beerwench"; ID 9536789; symbol: ![](http://img820.imageshack.us/img820/5931/tgtsym02.gif) PoE: "The Regal Personality"; targeted; T-15 User: "Tesla DC"; ID 12578717; symbol: ![](http://img219.imageshack.us/img219/5170/tgtsym03.gif) PoE: "The Troubled Mind"; targeted; T-14 User: "cheesehead"; ID 13979142; symbol: ![](http://img819.imageshack.us/img819/9397/tgtsym04.gif) PoE: "The Oft Wayward Academic"; targeted; T-13 User: "colleenz"; ID 9587989; symbol: ![](http://img130.imageshack.us/img130/5648/tgtsym05.gif) PoE: "The Industrious Puzzler"; targeted; T-12 I am sorry.
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Post by Virgil Showlion on Dec 23, 2010 2:38:19 GMT -5
IHearYou2Message #817 - 12/10/10 05:14 AMWith minimal analysis I'll say that there is mutiple locations to place the drunkards but the maximum distance they'll travel on the woody will always be a mile. Virgil SyonidMessage #818 - 12/10/10 05:28 AM locations to place the drunkards Now now. If you wish to refer to EEers as "drunkards", you'll have to provide a proof for the famous YM Conjecture: ![](http://img696.imageshack.us/img696/8415/ymconj.gif) As for solving the problem, I'm afraid the analysis is part of the solution. Still, you are correct. We'll let some of the others tackle it. ![](http://boards.msn.com/Themes/default/emoticons/wink_smile.gif) Virgil SyonidMessage #819 - 12/10/10 09:54 PMOK You2ube, since the others appear too chickenly (braawk!) to attempt a solution, I shall pose to you in particular a slightly more challenging problem. With 20 EEers on the plank, what is the largest number of "bumps" that can occur before all EEers leave the plank? ____________________ PoE: "The Loyal Denizen"; targeted; T-16 User: "beerwench"; ID 9536789; symbol: ![](http://img820.imageshack.us/img820/5931/tgtsym02.gif) PoE: "The Regal Personality"; targeted; T-15 User: "Tesla DC"; ID 12578717; symbol: ![](http://img219.imageshack.us/img219/5170/tgtsym03.gif) PoE: "The Troubled Mind"; targeted; T-14 User: "cheesehead"; ID 13979142; symbol: ![](http://img819.imageshack.us/img819/9397/tgtsym04.gif) PoE: "The Oft Wayward Academic"; targeted; T-13 User: "colleenz"; ID 9587989; symbol: ![](http://img130.imageshack.us/img130/5648/tgtsym05.gif) PoE: "The Industrious Puzzler"; targeted; T-12 User: "IHearYou2"; ID 1779581; symbol: ![](http://img683.imageshack.us/img683/4858/tgtsym06.gif) PoE: "The Fierce Moderator"; targeted; T-11 I am sorry. Snow Bunny SpriteMessage #820 - 12/10/10 11:02 PMThe Fierce Moderator OooOoooOoooohhhhh, did you just give IHOP a smite button? OK You2ube, since the others appear too chickenly (braawk!) to attempt a solution,
You already said that IHOP was right. Why would I waste my time when I could be drinking fluorinated water? ![](http://boards.msn.com/Themes/default/emoticons/tongue_smile.gif)
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Post by Virgil Showlion on Dec 23, 2010 2:38:50 GMT -5
Virgil SyonidMessage #821 - 12/11/10 02:25 AMYou already said that IHOP was right. Why would I waste my time when I could be drinking fluorinated water? The goal of a puzzle isn't to find the answer. It's to enrich one's intellect, scrimping and striving to establish order amid chaos. It's an affirmation that our Creator fashioned us as adaptable, infinitely curious beings. Besides, we all know you have that fluoride IV hooked up 24/7. I can picture you now: hunched in a wheelchair, the flesh barely clinging to your fluoridated bones as you reach a trembling gnarled claw toward the flow regulator for your IV. You've given up so much for your addiction. It's only natural you should defend it. ____________________ PoE: "The Loyal Denizen"; targeted; T-16 User: "beerwench"; ID 9536789; symbol: ![](http://img820.imageshack.us/img820/5931/tgtsym02.gif) PoE: "The Regal Personality"; targeted; T-15 User: "Tesla DC"; ID 12578717; symbol: ![](http://img219.imageshack.us/img219/5170/tgtsym03.gif) PoE: "The Troubled Mind"; targeted; T-14 User: "cheesehead"; ID 13979142; symbol: ![](http://img819.imageshack.us/img819/9397/tgtsym04.gif) PoE: "The Oft Wayward Academic"; targeted; T-13 User: "colleenz"; ID 9587989; symbol: ![](http://img130.imageshack.us/img130/5648/tgtsym05.gif) PoE: "The Industrious Puzzler"; targeted; T-12 User: "IHearYou2"; ID 1779581; symbol: ![](http://img683.imageshack.us/img683/4858/tgtsym06.gif) PoE: "The Fierce Moderator"; targeted; T-11 User: "Dr. Pig"; ID 11780093; symbol: ![](http://img573.imageshack.us/img573/6448/tgtsym11.gif) PoE: "The Seeker of Validation"; targeted; T-10 User: "SlowButSure"; ID 14638558; symbol: ![](http://img403.imageshack.us/img403/1492/tgtsym07.gif) PoE: "The Fluoridated One"; targeted; T-9 I am sorry.
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Post by Virgil Showlion on Dec 23, 2010 2:46:43 GMT -5
VirgilBot TP v0.01 Completed Thread Port - 810 post(s) in 13585 seconds.
Final post: Message #821 - 12/11/10 02:25 AM
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