CaptainEd

schlepping--oooo sanguinely--xxxo xenogeneic--oo manometers--xoo zabaglione--xxxoo scathingly--xxo rhinestone--xoo waveringly--xxxoo deodorants--ooooo xenografts--ooo phlegmatic--xoooo melancholy--xxo sanguinous--xx tangential--xoooo

schlepping--oooo sanguinely--xxxo xenogeneic--oo manometers--xoo zabaglione--xxxoo rhinestone--xoo deodorants--ooooo xenografts--ooo phlegmatic--xoooo melancholy--xxo sanguinous--xx tangential--xoooo

schlepping--oooo xenogeneic--oo zabaglione--xxxoo rhinestone--xoo deodorants--ooooo xenografts--ooo phlegmatic--xoooo melancholy--xxo sanguinous--xx Perhaps, Seeksit, you have found it again; thanks for the theme. It sets the tone for the one-line story, but I think I'll quit on that (besides, I'm worried about where Fred has his xenografts--he probably has buyer's remorse...)

schlepping--oooo xenogeneic--oo zabaglione--xxxoo rhinestone--xoo deodorants--ooooo xenografts--ooo Palmer, xenografts isn't so weird. What's weird is the one-line story I'm trying to build using all the words on the list. I was ok with "Schlepping some zabaglione made with xenogeneic cream, Fred began to feel remorse." (It reminds me of the old Dixieland classic "Struttin' with some Barbecue") And the rhinestone and deodorants (clearly other products in Fred's pushcart) were ok as well, but the xenografts are a bit chilling...

Palmer, how kind of you to offer me some zabaglione! And, a new word (xenogeneic)! This is fun, thanks! schlepping--oooo xenogeneic--oo zabaglione--xxxoo

Nobody, in the reduction ad absurdum case you propose (imagine a thick tape, like 1 inch), and we follow your accurate advice to recognize that each time around, the tape has to move to a new level and leave a bit of a gap, we have the problem that there is no longer a single radius anyway. Yet our OP gives us "the" radius, as if it is a close approximation. As long as we're imagining, let's go the opposite direction, imagine an infinitesimally thin tape, like .001 inch. The gap that the tape has to rise above is very small. Might as well just call it zero. If we pretend that it all smooths out, and there is simply a circle (as the OP implies), you can just measure the area, make a long thin rectangle out of it (as I proposed in my post a while back), and calculate the length. Don't need to distinguish whether there are concentric rings 0.02 inch thick or spirals, or even back and forth layers that never actually circumnavigate the spool. Just treat it as oatmeal. How long would this much oatmeal stretch if it were smooshed down to 0.02 in? In fact, let's go reduction ad absurdum the other way. Let's say I buy your observation that we must calculate the length of a spiral rather than circles. Given that the OP says "the" radius is 1 inch (or it says "the" diameter is 2, I forget what it says), and your observation depends on the fact that it is NOT a perfect circle, and hence has a varying diametric profile, then what diametric profile are YOU assuming for the spool plus tape? So, I'm not convinced that the entire thread is "all wrong".

Yeah, that's what I was afraid of! That's why I was in such a hurry. OK, gang, I've got a 10. WilsonsMum, dear thing, I know that you enjoy challenges, and are a very quick solver. And I know you don't like unfamiliar words. Well, two out of three ain't bad--this is NOT a familiar word. Ten letters, keep those cards and letters coming... SERIOUS EDIT: Changed 9 to 10. There are really 10 letters!

Yes, for this outstanding performance, you deserve a trophy!

Good Job! (edited to correct formatting)

Somebody doesn't get the problem. Maybe it's me.

Bushindo, as long as the prisoners are together the previous night, why don't they alphabetize all 100 of them, each learn his/her ordinal number, and THEN divide into two groups. As you say, have each prisoner memorize the names AND ORDINALS of the 50 people in his/her group. (I haven't considered how they should proceed on the day of the big test, but it feels like a more valuable bit of information...)

[spoiler='Or we could take the physicist's approach '], and just say, "how much area consists of tape, how long a rectangle would the tape be if the thickness were 1/50?" The area of the spool is pi. The area of the spool with tape on it is 4*pi. The area of the tape alone is 4*pi - pi = 3*pi If that area were a long skinny rectangle of thickness 1/50, its length would be 3*pi / (1/50) = 150*pi ~= 471.xxx inches

Lovely examples! Holy cow, FREEDOM doesn't even involve C or G. Looks like Gmaster and I have more to think about...

Hey, correct me if I'm wrong, P2 is safe even in a 100-cycle. Given the situation in my post #11, he has looked at his 50 jars: 100, 1, 51-98. He put the contents of 98 (which contains "99") into 100. He didn't find his number (because it's sitting in 99). So, when the warden says, "Where's your nametag?", P2 says, with certainty, "It's in jar 99". So, the only prisoner who has a chance of death, given HH's proposal, is P1. Regardless of whether P1 finds his number, all other prisoners are safe.

do you like PANIC EATING ICING BIG BICEP JAIL

Tedious detail: actually, the only way P2 can have a problem is for there to be an initial chain of 100 jars. I said the only way P2 can fail is if there are two chains of 50 or one chain of 100. I think that's false. Suppose there are two chains of 50. For simplicity, suppose J1 contains "2", J2 contains "3", and so on up to jar 50 containing "1". P1 wins, and P2 wins similarly. So two chains of 50 permit everyone to survive. Suppose one chain of 51 and one of 49. Once again J1=2, J2=3...J50=51, J51=1. Now P1 corrects J2-J50, and puts "51" in J1. Now comes P2, whose number happens to be 100, and suppose J52=53, J53=54...j99=100, j100=52. He starts with j100, and has to run through 49 jars, starting with 52. OK, he gets there on his 49th seek. So chains of 51,49 permit all but P1 to survive. The ONLY case where P2 can fail is if there's a chain of 100. Imagine j1=2, j2=3,...j99=100, j100=1. Now P1 opens J1-j50, and corrects j2-j50, leaving j1=51. Now comes P2 (whose number is 100). He opens 100, sees "1"; opens 1, sees "51", opens 51, sees "52", and so on. So he opens jar (50 + I) on his (I+2) look. So, on his 50th look, he's looking at 98. He, too fails, having corrected the rest of the deck, except for 99 and 100, which now point to each other. Note, a chain of 99 is not a problem for P2, because that leaves a chain of 1 which he'll skip over without looking at. (In the case above, if j99=99 to begin with, then j98=100, and he succeeds.)

Bushindo, that is an improvement, and I agree that HH's solution offers a slightly smaller expectation that 0.95 (I doubt it is as small as 0.9945, but I can't do the math to be sure). The worst case: the first prisoner goes through 50 jars without finding his number, then he is only able to correct 49 jars (he'll wind up putting some garbage number in his own jar). That means it is possible for the second prisoner to have the bad luck of chasing another chain of 50 jars without success. For this to happen, the remaining 50 have to form a chain, with P2's number at the end AND it is the number written on the slip that P1 had to put into his own jar. The probabilities, as we've seen before, are low: what is the probability of there being two permutation chains of length 50? That's why I think the expected value is still only a tiny bit less than 0.95. Of course, BellaxPallus offers a marvelous option as well! edit: once again, HH has typed quicker and thought deeper than I. Once again, I buy his argument. In fact, his probabilities are computed only for the worst case, and are not adjusted by the probability of that case coming to pass (ie, there are two chains of length 50 or one chain of length 100), so I think the actual expectation is a tad higher still.

I responded to Doug, but HoustonHokie typed faster and thought deeper than I did. I think I understand it. Good job again!

edit: I get it now. Good job!

I would propose neither. You've got an interesting puzzle going...I'm eager to keep thinking about it (admittedly I may not be quick about it, but at least I'm back from vacation...)

Nice counterexamples! I'm certainly shocked. The "cough, not cold", "arriverderci, not ciao" and "cage not cell" are particularly eye-opening. I've got to do some more head-scratching...

COUGH SOUGH NIGHT BOUGH ARRIVEDERCI