# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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Griffin
Daedalian Member

 Posted: Mon Mar 13, 2000 5:01 am    Post subject: 1 1. I can do it in 12 days. Can anyone do better? 2. You could go an infinite distance, couldn't you? (As long as you didn't die from old age, anyway)
araya
Daedalian Member

 Posted: Mon Mar 13, 2000 5:28 am    Post subject: 2 http://www.greylabyrinth.com/Puzzles/puzzle087.htm 1. I was thinking 15 days.. I'll look at it some more 2. Yeah, infinite distance, you can always move an arbitrary amount of food, say, a mile away from where you had the previous arbitrary amount.
Ghost Post
Icarian Member

 Posted: Mon Mar 13, 2000 10:36 am    Post subject: 3 1. 15 Days, can't see how you do it in 12 first trip - out 1, drop 1, back 1 2 days second trip - out 1, drop 1, back 1 2 days third trip - out 1, pickup 1, out 1, drop 1, back 1, pickup 1, back 1 4 days fourth trip - out 1, drop 1, back 1 2 days fifth trip - out 1, pickup 1, out 1, pickup 1, out 3 5 days 2+2+4+2+5=15 days 2. I concur, nothing says you have to go in a straight line, you could just circle around the oasis forever :-) This one seems a lot easier than last week's. I'm worried there's a catch. ------------------ Robert Wilkinson.
friskythepig
Guest

 Posted: Mon Mar 13, 2000 3:24 pm    Post subject: 4 I think you can do it in just under 12 days. I'll see if I can work out an exact solution.
HyToFry
Drama queen

Posted: Mon Mar 13, 2000 4:53 pm    Post subject: 5

Okay I get nine days..
heres why...

BEFORE YOU READ ANY FURTHER UNDERSTAND THE ANSWER TO THE QUESTION IS EXPLAINED AND I REALLY DID GET NINE DAYS, I DIDN'T JUST MAKE IT UP, IF YOU WAN'T TO SOLVE THE PUZZLE SKIP MY POST. Oh and don't blame me if you think i'm lying and i ruin the puzzle for you, after all I did warn you

from start point travel 20 miles WEST (actually it dosen't matter, its just fun to say head east at the end), drop off 1 days supply of food and travel back... thats 2 days

with 3 days supply, travel to the drop off point, pick up the food, travel another 20 miles, and if you haven't reached civilization, you have two days supply to get home.

If you do the math, thats 6 days.

Now You KNOW FOR A FACT THAT CIVILIZATION IS NO MORE THAN 60 MILES EAST (this is because civilization could be no more that 100 miles east of 40 miles west from you, because civilization can be no more that 100 miles from anywhere in the desert. ) with 3 days of food, you can travel 60 miles, so stock up and head east ...
Hope this is right.

Oh P.S. Don't let the Minotar trick you with the greater that 100 mile radius, the desert in question couldn't have a 100 mile radius, it has a 50 mile radius... hehe although it does have a 100 mile diamater

Oh and for part two i get 1 year, after that you would have a sunburn so bad you couldn't cary food any more
hehe just kidding INDEFINATELY, ie you could walk to the moon
(I think this question was only put in to throw us off to believe that the desert had a 100 mile RADIUS, when in fact it has a 50 mile radius, think about the second question never says the desert HAS a 100 mile radius, it only says "if it had a radius greater than 100 miles", it would be the same as saying "if it had a radius greater than 1000 miles")

 Quote: This one seems a lot easier than last week's. I'm worried there's a catch.

Not a catch, just a tricky way of thinking.

[This message has been edited by HyToFry (edited 03-13-2000).]
HyToFry
Drama queen

 Posted: Mon Mar 13, 2000 5:43 pm    Post subject: 6 Doing more thinking about this, I have to change my answer: It would take 1 day, because. There is no Desert, the oasis is your friend John's Fridge. You are not fooled, you grab a (soda/beer) and go sit on John's Couch. Oh and givin that the oasis, has an UNLIMITID supply of food/water (and if you want to get technicall UNLIMITED SUPPLIES is VERY vague, ie it could mean an unlimited supply of everything you need/want), WHY THE HELL WOULD YOU WANT TO LEAVE? ARE YOU INSANE, WAS THERE EVER AN OAISIS? Or just a Mirage? A sentence fragment. Another. A third.... sorry
friskythepig
Guest

 Posted: Mon Mar 13, 2000 5:53 pm    Post subject: 7 Good point, hadn't thought of that. However 7.5 days 30 miles east, go back - three days 10 miles west, drop off supply of food, go back - one day 70 miles west using the food stores enroute - 3.5 days. Any advances?
HyToFry
Drama queen

 Posted: Mon Mar 13, 2000 6:41 pm    Post subject: 8 Nope, not from me, I can't see any way of beating that OH P.S. After thinking about it i got 8 days, but 7.5 is < 8 so HEHE 8 days would be 20 east 20 west 2 days 20west-drop off 1 day-20 east. 20west, pickup, 20 west 20 west 20 west. Thats eight days However, when i came back to post my NEW one day shorter answer, i found i had been defeated ... Oh well, theres always 4/1 oh wait, maybe not, but lets hope soo.... [This message has been edited by HyToFry (edited 03-13-2000).]
Griffin
Daedalian Member

 Posted: Mon Mar 13, 2000 9:21 pm    Post subject: 9 The 12 day solution I was thinking of: Goto the 10 mile mark, leave 2 days worth of supplies, come back, and repeat. Eventually, you will be at the 10 mile mark in 3.5 days with 8.5 days worth of supplies. You then go between the 10 mile mark and the 20 mile mark. Eventually, you will have 6 days worth of supplies at the 20 mile mark, with 6 days having passed. Then you go to the forty mile mark, drop of a days worth of food, and come back (8 days have passed). You then head 80 straight miles to civilization (12 days). I can't beat the 7.5 days, however. It does seem as if the desert would only have a 50 mile radius (or smaller).
Ghost Post
Icarian Member

 Posted: Tue Mar 14, 2000 8:02 am    Post subject: 10 Wait a minute, you can't guarantee escape from the desert at all! What if your compass breaks, or you stumble and hurt your leg? While you can be sure of your direction, you can't be sure you're walking exactly 20 miles a day. You could only be walking 19.5 miles a day, leaving you 1.5 miles short of your destination. Therefore, only with a bit of good luck can you ensure success.
friskythepig
Daedalian Member

 Posted: Tue Mar 14, 2000 11:09 am    Post subject: 11 If you assume that you do have to travel 100 miles in one direction, it's an interesting problem to work out the optimum positions for your food/ water dumps. I was thinking that the first dump should be 3/7 of a days travel from the oasis ie 8.57 miles. The reason for this is you can then dump 15/7 days supplies and return to the oasis. This cache can then be used to exactly replenish your supplies on 5 further visits to dump 1. On your second trip from the oasis you travel 3/5 of a days travel beyond dump 1, replenishing supplies enroute. You can drop 9/5 days supplies at dump 2 and return to the oasis stopping at dump 1 on the way. On the third trip, dump 3 can be set up 3/3=1 day beyond dump 2 with one days supplies. On the fourth trip you should be able to reach civilisation. This allows you to travel 20*(3/7+3/5+3/3+3) = 100.57 miles As there are 7 trip either to or from dump 1, 5 trips to or from dump 2, 3 trips to or from dump 3 and one trip to civilisation, the total time taken is 4*3= 12 days. I'm not sure if this is the optimum way of doing it though.
HyToFry
Drama queen

 Posted: Tue Mar 14, 2000 3:25 pm    Post subject: 12 Ziggy, you make an interesting point, however this goes back to what i said, how do we even know that there is an oasis, and it's not just a mirage? For all we know we're drinking sand SO HAHA we're gonna die anywayz . Also if you think about it, it would be impossible to GUARENTEE we would ever get out, for all we know, we'll start executeing our plan, and get caught in another sand storm, and be lost with NO oasis. [This message has been edited by HyToFry (edited 03-14-2000).]
kitakaze
Daedalian Member

 Posted: Tue Mar 14, 2000 8:44 pm    Post subject: 13 The trouble I have with these problems is that, unless you really specify them carefully, you can make all kinds of assumptions. For example, on day one, you could eat breakfast, grab 3 days supply, travel for 1/2 a day (10 miles), drop off 2.67 days worth of food, eat lunch (1/3 of a days rations) and go home, and eat supper when you get home. I haven't worked this one through, yet, but it would provide a much shorter total trip. But the problem probably wants to assume a constant rate of supply usage. Kaze
Griffin
Daedalian Member

 Posted: Wed Mar 15, 2000 1:11 pm    Post subject: 14 Friskythepig, I think you have the right idea. But if you shift your entire solution towards the oasis so that you run out of supplys just as you reach civilization, it is faster. If you have your supply dumps at the 8 mile mark, the 20 mile mark, and the 40 mile mark, then I think you can do it in 11.8 days.
friskythepig
Daedalian Member

 Posted: Wed Mar 15, 2000 8:02 pm    Post subject: 15 Yep, I think 11.8 days is the quickest you could do it in. I noticed that the question says that before you get to the oasis, you had been 'wandering for days' ie. moving without purpose or direction. This doesn't seem like a sensible course of action given that when you got lost, you had a compass and limited supplies. Given that you're not stupid, it would have been more sensible to travel in a straight line 'for days' (ie 2 or 3 days ) in which case you should know that civilisation can't be more than 3 days travel in the same direction from the oasis. Frisky the pedant
Wonko the Sane
Daedalian Member

 Posted: Thu Mar 16, 2000 2:10 am    Post subject: 16 I agree with 7.5 days. I got in to this a little late so I guess i wont be the first one to post, 30 north then back, drop food at 10 south, then make the run. Alternate solution: There can't be a desert. There's an infinite supply of food and water. If that were true, then the oasis must cover the entire universe. Basically, you aren't going to be there in the first place because you've either sufficated or drowned long ago since you're either swimming/encased in water or food. Of course, perhaps Minotaur meant to say that this water and food is being spewed from a white hole that holds constant outward pressure that can be restricted by a certain mass of food/water. If that's true, then you're stuck in the desert for another 7.5 days, after which you can become immensly rich by telling people of your discovery of the universe's only locally concentrated white hole (and in fact the first real one ever discovered). So I guess you win out either way.
Greekst
Guest

 Posted: Fri Mar 17, 2000 1:56 pm    Post subject: 17 You don't have to go 30 miles north. About 18 should do it (assuming Puzzlania has the same curvature as the earth). This is because the horizon is about 12 miles away (from memory). Standing on a sand dune should help as would the height of an structures in "Civilisation".
HyToFry
Drama queen

 Posted: Fri Mar 17, 2000 8:45 pm    Post subject: 18 Okay if we include the horizon observation, we can do it in < 6 30 West - 30 East 3 days, and you know its no more that 58 miles east of you (because you could see 42 miles west), so Grab 3 days supply and head east, you should be able to walk 2 miles past the end of civilization But, as we all know, in a Puzzlainian desert it is impossible to see 1 foot in front of you [This message has been edited by HyToFry (edited 03-17-2000).]
abbey
Guest

 Posted: Thu Mar 23, 2000 11:05 pm    Post subject: 19 11 days to walk 100 miles. 1-take 3, walk to 20, eat. 2-leave 2, walk back, eat. (2 @ 20) 3-take 3, walk to 20, eat. (4 @ 20) 4-take 3, walk to 40, eat. (1 @ 20, 2 @ 40) 5-walk to 20, eat, (0 @ 20, 2 @ 40) 6-walk back, eat. (0 @ 20, 2 @ 40) 7-take 3, walk to 20, eat. (2 @ 20, 2 @ 40) 8-take 2, walk to 40, eat. (3 @ 40) 9-take 3, walk to 60, eat. (2 @ 60) 10-take 2, walk to 80, eat. (1 @ 80) 11-walk out, eat.
HyToFry
Drama queen

 Posted: Fri Mar 24, 2000 7:25 pm    Post subject: 20 abbey, this is assuming that you don't have to eat during the trip If we assume this, then. Day 1 20 east, eat, Day 2 20 west, eat, (back at starting point now we know that civilization is nomore than 80 miles west of us. Day 3 20 west, eat, 2 day supply left. Day 4 20 west, eat, 1 day supply left. Day 5 20 west, eat, No Supplys. Day 6 20 wast, eat at town. 6 Days again If you figure in the horizon in this case, you could do it in < 5 Days 8 east - 8 west, not even 1 day has passed, then take it from Day 3 of the previous solution; you would be able to walk 4 miles past the end of town before needing to eat. [This message has been edited by HyToFry (edited 03-24-2000).]
Corey
Guest

 Posted: Fri Mar 24, 2000 8:39 pm    Post subject: 21 I think the desert has a 100 mile radius because no point IN the desert is more than 100 miles from the edge. If it had a 100 mile diameter,the Minotaur would have said 50 miles from the edge.
Quailman
His Postmajesty

 Posted: Fri Mar 24, 2000 9:18 pm    Post subject: 22 Corey: When I first read this puzzle, I thought as you did, but the minotaur said that "Fortunately, you know that no part of the desert is more than a hundred miles in any direction from civilization." Someone pointed out that if you traveled 30 miles (1 day) east, then the edge can't be more than 100 miles to the west, or 70 miles from your original position. Therefor, if you do a 3 day round trip (1 1/2 each way) in one direction, you only have to go a maximum of 70 the other way. I still like Griffin's 12 day solution, but HyToFry has a valid point.
Ghost Post
Icarian Member

 Posted: Fri Mar 24, 2000 10:41 pm    Post subject: 23 12 days is the answer. You make stocks at 8 , 20 , 40 miles from oasis. You move 7*(8 - 0) + 5*(20 - 8) + 3*(40 - 20) + 1*(100 - 40) = 236 miles. 236 is actually 240 , so 240/20 = 12 days. email me if you need better explanation. Answer to the second question is : Infinite distance.(I think so). You can see similar problem in Martin Gardner's "Mathematical diversions" book.
HyToFry
Drama queen

 Posted: Sat Mar 25, 2000 12:04 am    Post subject: 24 Abbey, I did some more thinking about the way you interperate the problem. If you assume that you don't have to eat until the end of the day, you can walk 100 miles in one direction in 7 Days Day 1, Out 20, Drop 2, eat 1 Day 2, Back 20, Eat, Stock Up 3 Day 3, Out 20, Eat one of the days supply that you dropped, now you have 4, but can only carry 3 Day 4, Out 20 more, now your 40 out, eat one, so you have 2 left Day 5, Out 20 more, now out 60, eat one, still have one left Day 6, Out 20 more, now out 80, eat your last one.. Day 7, Out the finale 20, eat when you get to town, thats 100 miles in one direction, assuming that you eat at the end of the 20 miles. and I'm not even going to go into what would happen if you assumed the horizon on this one
Wonko the Sane
Daedalian Member

 Posted: Tue Mar 28, 2000 1:37 am    Post subject: 25 Sorry HyToFry, I think the puzzle means that if you don't get food exactly every 20 miles you drop dead. You don't get a millimeter either way. To make it, you have to either have extra food or collapse at the border. ------------------ It's not the size of the spork, it's whether or not it's made of #7 recyclable plastic.
HyToFry
Drama queen

 Posted: Tue Mar 28, 2000 9:33 pm    Post subject: 26 HeHe, Wonko I know that I'm just stateing that you can walk 100 miles in 7 days if you assume that you don't have to eat until the end of the trip, I still like the 7.5 Day answer the most, but i'm pretty sure that Minotar was looking for the 12 day answer. The Riddle should have said "You know that NO part of the Desert is more than 100 miles to the East of Civ... which is to say that Civ could be NO more than 100 miles west of you , but since he didn't 7.5 days is the fastest you could do it assumeing that you have to use food as you walk, 6 days if you can eat at the end of the trip, and just under 12 if you assume that you have to walk in one direction; and have to eat as you go. The quickest is just under 5 days, thats using the horizon theory and assumeing that you eat at the end of the trip
Khayman
Guest

 Posted: Tue Mar 28, 2000 10:57 pm    Post subject: 27 p1)Can't you do it in 11? The trick is to eat the day's worth of food before you leave... 1)Eat. Carry 3 days food. Travel 20 miles. (+20) 2)Drop 2 days food. Eat days food. Travel back to oasis. (+0) 3)Eat. Carry 3 days food. Travel 20 miles.(+20) 4)Eat. Pickup 1 days food. Carry 3 days food. Travel 20 miles.(+40) 5)Drop 2 days food. Eat days food. Travel back 20 miles. (+20) 6)Pick up days food and eat it. Travel back to oasis.(+0) 7)Eat. Carry 3 days food. Travel 20 miles.(+20) 8)Eat. Carry 2 days food. Travel 20 miles. (+40) 9)Eat. Pick up 2 days food. Now carrying 3 days food. Travel 20 miles. (+60) 10)Eat. Carry 2 days food. Travel 20 miles.(+80) 11)Eat. Carry 1 days food. Travel 20 miles. (+100) Reach civilization & sue your travel agent. p2)Yes infinite... spend (20/infinity)*eternity moving the oasis from where it is to a spot 20 miles away... then repeat
Wonko the Sane
Daedalian Member

 Posted: Wed Mar 29, 2000 12:01 am    Post subject: 28 Actually. I think this is how he should have stated it. "You got sucked in to a vaccuum and you have no idea exactly how. You do know that no part is more than 100 miles in any direction from a breathable atmosphere. You've happened to find an oases of oxygen tanks capable of supporting you for a day. You can only carry three at a time. How long is it until you can take the mask off without sufficating? =)
Mathieu
Guest

 Posted: Wed Mar 29, 2000 12:16 am    Post subject: 29 Fogive me, but couldn't it be done in 5? Just take your 3 day supply, in any direction. Walk 60 miles (3 days), and "Oh no, out of food and water." Walk for 2 more days, and you still have about one day to live before requiring water, and a dozen or so before needing food.
Mathieu
Guest

 Posted: Wed Mar 29, 2000 4:37 am    Post subject: 30 Well, of course it won't work in the vaccuum example above though. I thought that "Fogive me" looked a bit funny when I typed it! -Forgive me!
Ghost Post
Icarian Member

 Posted: Wed Mar 29, 2000 5:11 am    Post subject: 31 Registered! this is a test... -any others? -sorry, I'm just getting myself excited... -I'm done now. [This message has been edited {I can edit this part too!} by Mathieu (edited 03-29-2000).] [This message has been edited by Mathieu (edited 03-29-2000).]
Aaron
Daedalian Member

 Posted: Wed Mar 29, 2000 10:52 am    Post subject: 32 Check the FAQ's, Mathieu.
HyToFry
Drama queen

 Posted: Wed Mar 29, 2000 3:17 pm    Post subject: 33 Kyahman going off of your logic, you could do it in seven days day 1 eat-out 20-drop off 2 days supply day 2 eat-back 20 - pick up 3 days day 3 eat-out 20 (with 3 days supply) now your out 20 with 5 days of food day 4 eat-carry 3 days of food and out 40 day 5 eat-2 days supplies left-out to 60 day 6 eat-1 day left- out to 80 day 7 eat-nothing left-out to 100 or civilisation. I like what Wonko said about the vacuum though, it makes it harder to screw up the question, but i was thinking Your stuck on the moon......and for some reason you can jump EXACTLY 20 miles, but you can only carry enough air to do this 3 times, (this makes it even more complex because you can't stop after 10 miles hehe)
Wonko the Sane
Daedalian Member

 Posted: Thu Mar 30, 2000 1:42 am    Post subject: 34 Good example there too. Basically, something to prevent abuse of the problem though. Actually, I think being able to go portions of 20 miles is really a better way to do it. More complex like that, I think.
hank
Daedalian Member

 Posted: Sat Apr 01, 2000 3:51 pm    Post subject: 35 day1. head north for twenty miles and still in desert at Point Nowhere day2. return to oasis day3. head south and eat meal#1 at 40 miles south of Pt. Nowhere(20 miles from oasis) day4. head south and eat meal#2 at 60 miles south of Pt. Nowhere day5. head south and eat meal#3 at 80 miles south of Pt. Nowhere day6. head south and eat at MacDonalds at 100 miles south of Pt Nowhere. Six days easy. Where did I go wrong?
Wonko the Sane
Daedalian Member

 Posted: Sun Apr 02, 2000 10:41 pm    Post subject: 36 You forgot a step (I marked with with a -) it should be day1. head north for twenty miles and still in desert at Point Nowhere day2. return to oasis day3. head south and eat meal#1 at 40 miles south of Pt. Nowhere(20 miles from oasis) day4. head south and eat meal#2 at 60 miles south of Pt. Nowhere day5. head south and eat meal#3 at 80 miles south of Pt. Nowhere day6. head south and eat at MacDonalds at 100 miles south of Pt Nowhere. You went wrong in that you need to have 4 days of food to do this. You have to have the food as you travel or you can't go 20 miles. We went through this before...you have to assume that the food runs out at a steady rate.
Ghost Post
Icarian Member

 Posted: Wed Nov 22, 2000 8:55 pm    Post subject: 37 Lawrence of Puzzlania When I first read the Lawrence of Puzzlania puzzle, I thought just as everyone else did. However after close inspection, several holes in the logic of the "ANSWER" appeared. I have listed these below. If anyone finds any problems with my logic or reasoning, please feel free to post and let me know. #1. The puzzle states… "…no part of the desert is more than a hundred miles in any direction from civilization." Rearranging the sentence might help it become clearer. In any direction from civilization, no part of the desert is more than a hundred miles. [away]. "Civilization" is not outside of the desert, but rather in the middle. #2. The next problem is that Lawrence is LOST! Many of the posted solutions, and even the "official" solution(s) seemed to think that being lost, means that you know where you are. The first "official" solution assumes that the oasis is in the center of the desert. That information is not given, and in no way can it be presumed to be true. Remember, Good'ol Lawrence has no Idea where he is. #2-b This solution goes on to say that to get out of the desert in the fastest amount of time. Lawrence must run out of food and water just as he exits the desert. This would logically put him 60 miles from the edge of the desert. However, last time I checked, a compass does not measure long range distances. Lawrence would have to start at the edge of the desert and walk into it, to accurately find a place 60 miles inside of the desert. Although, if he were at the edge of the desert, he wouldn't be in this situation. The solution continues to work its way BACKWARD from there. #3 I mentioned earlier, in "#1", that the "civilization" had to be in the middle of the desert. This is not entirely correct howsoever. "civilization", would only HAVE to be in the middle if the desert was round and had a radius of 100 miles. In truth, the size and shape of the desert were not specified. The "civilization", in a smaller desert, could be anywhere inside, and still conform to the "rules" #3-b My last main [nit-picky] point is that the size or number of "civilization" are never given. Picture in your mind a city surrounded by a desert with a 100-mile radius. Now place a similar city and desert next to the first, overlapping the deserts. And then a third city and desert overlapping the second……….etc. This "simulation" gives a new view to the puzzle that was previously not explored. I believe that the puzzle is not possible to solve accurately with the information given. Thank you for reading my thoughts on the issue of this puzzle. I look forward to reading follow-up posts, and responding to them. Have a Puzzlania day. Raven
hank
Daedalian Member

 Posted: Wed Nov 22, 2000 9:17 pm    Post subject: 38 As best as I can understand, Raven your entire arguement stems from your rearranging the sentence. Don't ! Now we are back to the original problem which has been solved. By the way, If civilization existed in the mddle of the desert, there would be roads in the desert.
Ghost Post
Icarian Member

 Posted: Wed Nov 22, 2000 9:23 pm    Post subject: 39 roads in the desert? sounds nit-picky to me. Not all of my arguments stem from reading the sentence correctly. My argument that the official solution is wrong, and my argument that the oasis is not necessarily in the middle, AND my argument that Lawrence does not know where he is, all are not connected to my "sentence" argument. I dont THINK, that anyone can disprove that stuff, but then again I am not perfect, and this is what the forum is all about :-) Raven
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