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Post by Virgil Showlion on Dec 23, 2010 1:39:51 GMT -5
Gameshow Message #477 - 06/16/10 08:35 PM
Actually it does matter... I use to think the same way, my chances of picking the correct "door" now stood 50/50, so what difference would it make to switch.
However, By introducing a door that doesn't have the prize, your odds do change if you choose to swtich or not
I think Virgil had a similar brain teaser about this subject earlier, although it would be difficult to locate among the 40 pages.
When broken down, it looks like this.
Let's say the prize is in door A and not in Door B or C.
If you didn't change: You choose A, Monty shows you door C, you keep door A (Winner) You choose B, Monty shows you C, you keep B (Loser) You choose C, Monty shows you B (not going to show you A), you keep C (loser)
If you did change:
You choose A, Monty shows C, you switch to B (Loser) You choose B, Monty shows C, you switch to A (winner) You choose C, Monty shows B, you switch to A (winner)
Notice how you have a better chance of winning by switching than not switching.
My 2 cents
Ben
tall_guy Message #478 - 06/17/10 04:30 AM
For problem 36 statistically you should switch. When you chose envelope B it had a 33% chance, 1 in 3. Envelope A has a 50% chance, 1 in 2.
And laterbloomer, Re: #471... don't be so sure.
I'd say that it doesn't matter, since both choices have a 50/50 shot.
As odd as it seems, A actually has a 66.67% chance. Because the total must equal 100%, and the probability of B has not changed (still 33.33%) A must now equal 66.67. If C had been correct, A would have been the choice eliminated. It is not random.
Put another way, the initial probability for each choice is 33.33%. If you choose B, then the combined probabilities of A and C = 66.67%. If C is then determined to be zero, then the combined 66.67% belongs all to A.
Virgil Syonid Message #479 - 06/17/10 04:08 PM
(Solution to Problem 36)
Some excellent participation on this one.
To beerwench's eternal credit, she is CORRECT, and all other responses/explanations are INCORRECT. (Seriously!)
There is no benefit to switching from B to A. They both have a 50% chance of being correct.
This problem is not isomorphic to (i.e. analogous to) the Monty Hall problem, in which switching will better your odds.
The reason is because the teacher does not know (and therefore does not take into consideration) your answer before declaring one of the answers to be wrong.
In the Monty Hall case, Monty knows which door you've picked and he eliminates "the wrong door that is not yours". By preventing him from eliminating one of the doors, you've forced him into exposing additional information about the problem. In the test case, your teacher simply eliminates "one wrong answer", which might be yours or might not be yours. Since this elimination would occur surely either before or after you picked 'B', it's effectively the same thing as answer 'C' not existing at all.
And if you think about it, the 'Monty Hall' structure is a bit silly in this case. Suppose your buddy adds a fake answer 'D' to all of your questions before the exam starts. At the end of the exam, he whispers, "Psst. Hey. D is fake. Just replace any D you picked with an A or B or C. And any time you didn't pick D, switch your answer to something else."
If the Monty Hall structure was correct, your buddy's gambit would significantly improve your grade!
Virgil Syonid Message #480 - 06/17/10 04:11 PM
Problem 37 - Memento Mori
Can laterally-thinking EE'ers explain these strange deaths...
A man is found dead in the middle of a desert. He is found clutching a burnt-out match. How did he die?
Jack and Jill are found in the middle of a room, dead. Glass and water are everywhere. There are no windows, and the room was locked prior to the discovery. How did they die?
A man and a woman are driving in their car when it breaks down. The man decides to go for help at a gas station a few miles back. He makes sure nobody's in the car, rolls all the windows up, and locks all of the sedan's doors. He goes off, but when he comes back his wife is dead and there's a stranger in the car. The car has suffered no physical damage or tampering, so how did the stranger get in? And how did his wife die?
An old beggar who lived near the railroad tracks is found dead, apparently run over by a train. Bill, the beggar's only son, is summoned to make a positive identification of the body. The coroner is shocked when Bill witnesses the beggar's body and exclaims, "But... this isn't my father!" How did the beggar really die?
SBS is found gnawed to death. She is surrounded by beaver tracks, as well as spalling marks on the concrete from jetpacks. How did she die?
Post by Virgil Showlion on Dec 23, 2010 1:40:42 GMT -5
beerwench over 29000 bits of drivel posted Message #481 - 06/17/10 04:16 PM
To beerwench's eternal credit, she is CORRECT
*faint*
beerwench over 29000 bits of drivel posted Message #482 - 06/17/10 04:17 PM
SBS is found gnawed to death. She is surrounded by beaver tracks, as well as spalling marks on the concrete from jetpacks. How did she die?
POTD
genuine ga peach Message #483 - 06/17/10 04:32 PM
SBS is found gnawed to death. She is surrounded by beaver tracks, as well as spalling marks on the concrete from jetpacks. How did she die?
after she overdosed on COKE, the Canadian beavers had an SBS roast. Unfortunately, Canadians have no sense of humour, so they took this term literally
SbS, you know I you....really!
Gameshow Message #484 - 06/17/10 04:50 PM
Taking a stab at #1..
Person dies in desert clutching a match. I'm going to say he froze to death. Technically, a desert is any place that lacks precipitation. So, I guess a frozen tundra or arctic land could be a desert. Hence, he clutched a burnt match because that was his last source of heat before he froze.
Post by Virgil Showlion on Dec 23, 2010 1:41:12 GMT -5
SlowbutSure Message #485 - 06/17/10 06:24 PM
Oooooh, I actually like these types of problems. No time right now, so don't post the answers before 7:00 p.m. MST or so. Pretty please? With maple syrup on top?
An old beggar who lived near the railroad tracks is found dead, apparently run over by a train. Bill, the beggar's only son, is summoned to make a positive identification of the body. The coroner is shocked when Bill witnesses the beggar's body and exclaims, "But... this isn't my father!" How did the beggar really die?
Wait, what if the old beggar is his mother? Are you discriminating again?
SBS is found gnawed to death. She is surrounded by beaver tracks, as well as spalling marks on the concrete from jetpacks. How did she die?
LMAO! Hmmm... no maple syrup residue so I betcha it was Little Timmy's big brother, but I'll think about it later.
tall_guy Message #486 - 06/18/10 01:44 AM
This problem is not isomorphic to (i.e. analogous to) the Monty Hall problem, in which switching will better your odds.
What??!! You mean I am supposed to actually READ the problem first??!! That is going to cut down the fun considerably.
Virgil Syonid Message #487 - 06/22/10 05:47 PM
(Solution to Problem 37)
Gameshow nailed #1: Froze to death. (Although, GS, nearly any desert can drop to near-freezing temperatures overnight. They don't necessarily have to tundras.)
SBS got #4. The beggar is a woman. Like 'surgeon' and 'banker', 'beggar' carries a male stigma.
Others are:
2. Jack and Jill are goldfish. Their fishbowl broke.
3. The woman died shortly after giving birth.
5. SBS was, alas, 'taken out' by the 125th Royal Canadian Aerial Beaver Squadron. Witnesses reported her final words to be: "Beavers! So many beavers! Muscle Up, save me!"
Virgil Syonid Message #488 - 06/22/10 05:48 PM
Problem 38 - Battle of the Sexes
Some more riddles... but with a twist.
There's been far too much misandry on the EE boards lately. Since I hold a Y chromosome myself, I propose the following challenge:
Attempt to answer any of the following four riddles.
If you get a riddle right, I'll post an eloquent one-paragraph summary of your most laudable qualities.
If you get a riddle wrong, you must choose a male poster (not yourself) on the EE board and post an eloquent one-paragraph summary of that poster's most laudable qualities.
And to make things fair: no Googling answers.
Simple.
The riddles:
Give an 8-letter word with kst in the middle, in the beginning, and at the end.
An electric train is going North, and the wind is blowing South. Which way does the smoke go?
Three words in this sentence are mispelled. Which ones are they?
A depressed EE'er is on the 22nd floor of an office building, staring dismally and longingly through a dirty window. Finally, deciding to end it all, the EE'er opens the window, takes a deep breath, and jumps through it.
Outside the window is a sheer drop 22 stories down to a concrete sidewalk. The EE'er has nothing to cushion her fall or to slow her descent. Yet miraculously, when she hits the ground she is alive, unharmed, and happier than she's been in a long time.
Post by Virgil Showlion on Dec 23, 2010 1:41:43 GMT -5
Scottish_Lassie Message #489 - 06/22/10 05:54 PM
#2 - An electric train is going North, and the wind is blowing South. Which way does the smoke go?
There IS no smoke because it's an electric train.
beerwench over 29000 bits of drivel posted Message #490 - 06/22/10 05:54 PM
Outside the window is a sheer drop 22 stories down to a concrete sidewalk. The EE'er has nothing to cushion her fall or to slow her descent. Yet miraculously, when she hits the ground she is alive, unharmed, and happier than she's been in a long time.
How can this be?
Giant vat of beer (or alcohol of EErs choice) on the sidewalk?
Same reason that drunk drivers don't get as banged up -- you are less likely to resist at impact when you're toasted.
Or it is because Bumbles bounce? I always get those two mixed up.
The EEr landed on the roof of the building next door!
Scottish_Lassie Message #491 - 06/22/10 06:04 PM
A depressed EE'er is on the 22nd floor of an office building, staring dismally and longingly through a dirty window. Finally, deciding to end it all, the EE'er opens the window, takes a deep breath, and jumps through it.
Outside the window is a sheer drop 22 stories down to a concrete sidewalk. The EE'er has nothing to cushion her fall or to slow her descent. Yet miraculously, when she hits the ground she is alive, unharmed, and happier than she's been in a long time.
How can this be?
The depressed EE'er is STILL on the 22nd floor. She opened the window before jumping through it. So when she jumps through the window (i.e.the glass) she will land on the ledge of the 22nd floor.
Virgil Syonid Message #492 - 06/22/10 06:06 PM
There IS no smoke because it's an electric train.
Incorrect, unfortunately.
The smoke heads south with the wind. I never said the smoke came from the train.
Post by Virgil Showlion on Dec 23, 2010 1:42:33 GMT -5
Virgil Syonid Message #493 - 06/22/10 06:09 PM
The depressed EE'er is STILL on the 22nd floor. She opened the window before jumping. So when she jumps through the window (i.e.the glass) she will land on the ledge.
Hint: There is no ledge!
Giant vat of beer (or alcohol of EErs choice) on the sidewalk?
Hint: The reason the EE'er is happy at the end is alcohol-related.
Collenz: wisest and fairest of the brainteaser solvers. This one shines like a glowing beacon of wisdom, enlightening all whom she meets. A truly sagacious and learned woman, exercising her solving supremacy without the aid of search engines or hint books. Puzzles fall before her like many grains of sand caught in the winds of a class-5 hurricane. A victor in all aspects of life: spiritual, social, mental, and physical. Truly, the MSN boards have known no more formidable a lady.
Post by Virgil Showlion on Dec 23, 2010 1:43:04 GMT -5
Virgil Syonid Message #497 - 06/22/10 06:43 PM
#3 miss, spelled, and misspelled
Not quite sure I follow you.
IHearYou2 Message #498 - 06/22/10 06:47 PM
Mispelled should be misspelled and inside misspelled is a conjunction of two words miss and spelled tht get spelled incorrectly.
Virgil Syonid Message #499 - 06/22/10 06:58 PM
But then it would be: Three words in this sentence are miss spelled.
Unless you know Ms. Spelled personally, of course.
Virgil Syonid Message #500 - 06/23/10 10:25 PM
(Solution to Problem 38)
Some hits and some misses.
Colleenz gives the correct answer in #494. My encomium follows in #495.
The smoke blows south. Scottish_Lassie still owes us a pro-male paragraph for her attempted solution in #489.
The words 'Three' (should be spelled 'Two') and 'mispelled' (should be spelled 'misspelled') are misspelled. Some... unusual attempts at this one.
Good attempts by Queen beerwench and Scottish_Lassie. The 'correct' answer is that the EE'er is a window washer. She's washing the 22nd floor of a building. She sees a corporate minibar inside the building, decides that instant to quit her labour-intensive job, jumps through the window (from her platform on the outside) and goes to town on the liquor stock.
Post by Virgil Showlion on Dec 23, 2010 1:43:34 GMT -5
Virgil Syonid Message #501 - 06/23/10 10:27 PM
Problem 39 - So You Think You Know English?
Given the popularity of word problems on EE, it would appear that most EE'ers aren't too shabby with their English. But can they come up with the answers to these devious English-related questions?
Can you name at least one word whose pronunciation changes when you capitalize the first letter? (+5 Points Per Answer)
Name at least one word that contains all of the vowels (including 'y') in the same order as they appear in the alphabet. (+5 Points per Answer)
What is the only adjective in the English language that is written differently for males than it is for females? (+10 Points)
"Herein" has the distinction of being the English word with the greatest number of sub-words (contiguous shorter words) inside of it. How many sub-words does it have? (+5 Points for the Number) (+10 Points for Naming them All)
What is so unusual about a deified racecar? (+5 Points)
Can you name: a) an 8-letter word with 4 f's (think about the crowd at Everything Else), b) an 8-letter word with 4 g's, c) a 6-letter word with 4 u's (think Homer Simpson)? (+5 Points for Each Answer)
IHearYou2 Message #502 - 06/23/10 10:31 PM
#5 ooh ooh its a palindrome ooh ooh BOOYAH!!
.moonbeam3. Message #503 - 06/23/10 11:08 PM
partial spoilers - #3 (?) #4, #6
#3- "male" and "female" themselves can be adjectives, can't they? As in, "The male/female monkey is eating."
#4 Herein has 6 sub-words that i found : he her here ere rein in
Post by Virgil Showlion on Dec 23, 2010 1:45:22 GMT -5
weltschmerz Message #505 - 06/23/10 11:42 PM
Name at least one word that contains all of the vowels (including 'y') in the same order as they appear in the alphabet. (+5 Points per Answer)
FACETIOUSLY
IHearYou2 Message #506 - 06/23/10 11:47 PM
6c
Muumuu
Virgil Syonid Message #507 - 06/24/10 12:56 AM
Excellent. So far, we have:
1 2 3 4 5 6 Total IHearYou2
5 5 10 .moonbeam.
5
5 10 Gameshow
5 5 weltshmerz 5
5
Moonbeam gets +5 points for a valid-but-not-quite-what-we-were-looking-for answer in problem 3. Specifically, we're looking for an adjective whose purpose isn't to define or imply a gender. (Other examples of this would include 'masculine/feminine', 'boyish/girlish', etc.) The adjective I'm looking for has the same meaning when applied to men or women; it's just spelled differently in the two cases.
Also, moonbeam missed two of the sub-words in problem 4. (Although she inadvertently included one of the two in her solution.) I guarantee you that any hardcore Scrabble player can tell you the last one.
weltschmerz Message #508 - 06/24/10 01:29 AM
Can you name at least one word whose pronunciation changes when you capitalize the first letter?
Post by Virgil Showlion on Dec 23, 2010 1:45:52 GMT -5
weltschmerz Message #509 - 06/24/10 01:32 AM
Polish/polish?
When my sister was little, she wrote in her diary that she got her first bottle of nail Polish, and I remember teasing her about it.
.moonbeam3. Message #510 - 06/24/10 01:39 AM
Virgil, you're cheating me on points... #6, you said +5 for each answer, and i answered a and b.. and yes.. goggling is a word. i looked it up before i posted it lol
Virgil Syonid Message #511 - 06/24/10 02:05 AM
The masses are restless.
1 2 3 4 5 6 Total .moonbeam.
5
10 15 IHearYou2
5 5 10 weltshmerz 5 5
10 Gameshow
5 5 Yes, apparently 'goggling' is a word.
When my sister was little, she wrote in her diary that she got her first bottle of nail Polish, and I remember teasing her about it.
I have a younger sister too. She wrote a school essay about her trip to 'Sandy Eggo' (seriously).
Post by Virgil Showlion on Dec 23, 2010 1:47:13 GMT -5
Virgil Syonid Message #517 - 06/24/10 06:23 AM
I'll give you another one emeritus/emerita
I'll be darned. We'll have to edit the Wikipedia entry. It claims blond/blonde and brunet/brunette are the only ones. (Note that emeritus/emerita might not be considered 'fair' adjectives since they're postpositional. Also, the latter is considered strictly Latin by some dictionaries.)
Herein also has the letter i, which, if capitalized, also counts as a word. Not sure if it fits the rules of this game, though.
It does. 'Er' isn't recognized as one of the words in the original puzzle (likely because it's informal). 'Re' and 'I' are the correct two. (+5 for moonbeam and +10 for marco)
what are you owed an apology for ihop?
Not sure about that myself.
The new standings are:
1 2 3 4 5 6 Total IHearYou2
20 5 5 30 .moonbeam.
5 5 10 20 weltshmerz 5 5
10 marcopolo.121
10
10 Gameshow
5 5
weltschmerz Message #518 - 06/24/10 07:06 AM
What is the only adjective in the English language that is written differently for males than it is for females?
Hmmm...how about "spinster"?
As in "She has a spinster daughter". It's never a spinster son now, is it?
IHearYou2 Message #519 - 06/24/10 03:36 PM
The big V owes me an apology and needs to do four laps around the oval since he said there was only one adjective. He can't keep on passing out this misinformation and relying on Wiki as a reliable source.
Virgil Syonid Message #520 - 06/24/10 04:12 PM
The big V owes me an apology and needs to do four laps around the oval since he said there was only one adjective.
Post by Virgil Showlion on Dec 23, 2010 1:48:13 GMT -5
IHearYou2 Message #525 - 06/24/10 04:55 PM
moonbeam you need to bow to my mental fortitude, acuteness of thought, the supremacy of my reasoning, and the depth of my knowledge...this doesn't all have to happen at once but over the next week it would be nice..
whiskmav Message #526 - 06/24/10 04:56 PM
Give an 8-letter word with kst in the middle, in the beginning, and at the end.
Backstab
.moonbeam3. Message #527 - 06/24/10 05:01 PM
ihop, now you sound like MU lol.... he likes to think that men are superior too...
Post by Virgil Showlion on Dec 23, 2010 1:52:04 GMT -5
Virgil Syonid Message #529 - 06/24/10 11:00 PM
(Solution to Problem 39)
Moonbeam, IHearYou2, weltshmerz, marcopolo, and Gameshow provide the correct answers to problem 39 over the many posts following the problem statement.
Moonbeam is the problem champion, having accrued an impressive 35 points! First prize is a non-transferrable coupon for 50%-off all prostate examinations.
IHearYou2 earns the 'proved Wikipedia wrong' special honours.
All contributors are commended for their efforts.
But do any of these contributors possess the courage, the fortitude, the indefatigable Canadian work ethic, to attempt...
Virgil Syonid Message #530 - 06/24/10 11:02 PM
Problem 40 - SPECIAL PRIZE PROBLEM - Carpet Diem
To avoid the 125th Royal Canadian Aerial Beaver Brigade, SlowButSure (SBS) cowers beneath a 12' by 9' piece of carpet while the brigade flies overhead with their jetpacks.
When the threat has passed, SBS gets out from under the carpet and discovers that the middle has been singed. She quickly cuts an 8' by 1' piece out of the middle of the carpet to remove the singed fabric (see below).
After that, SBS wants to cut the carpet into only two pieces that she can sew together to form a 10' x 10' square.
What do these two pieces look like (i.e. how should the rug be cut)?
---=== SPECIAL PRIZE PROBLEM ===---
Since this problem requires some good thinking, I pledge to donate $100 to the (registered) charity of choice of the first person to post the correct solution.
The caveat is that you cannot search for the solution on the Internet (or get somebody else to solve it, or know the solution in advance, etc.). You MUST use your OWN beautiful God-given brain to figure it out.
IHearYou2 Message #531 - 06/24/10 11:13 PM
Is "Help Dora find her way home" a legitimate 501(c) charity that will work otherwise I don't want to think that much?
Post by Virgil Showlion on Dec 23, 2010 1:52:34 GMT -5
.moonbeam3. Message #533 - 06/25/10 01:22 AM
First prize is a non-transferrable coupon for 50%-off all prostate examinations.
ummm thanks Virgil.. but i have no prostate.. and all else i would normally say along with that statement shall, sadly, go unsaid as it would earn me a timeout fo' shizzle.
Well. Isn't that unfortunate! Had I but known! The highly valuable and regrettably non-transferable prize I'd saved up for the contest winner won't be of any use to you. I'd better hold onto it.
What a pity.
.moonbeam3. Message #536 - 06/25/10 01:52 AM
oh come on virgil. surely you can pony up for a boob squishin' instead.. them are always a good time!!!
and don't think i didn't notice your enthusiasm at being able to use the other one yourself...
Post by Virgil Showlion on Dec 23, 2010 1:54:26 GMT -5
Virgil Syonid Message #545 - 06/29/10 06:08 PM
I'll be cookin' one up later this evening.
whiskmav Message #546 - 06/29/10 08:57 PM
In the meantime...
White to play and mate in 2 moves
Virgil Syonid Message #547 - 06/30/10 12:24 AM
I'm leaving problem 40 'open' for now, and posting another hint later tonight.
For now, there's...
Virgil Syonid Message #548 - 06/30/10 12:26 AM
Problem 41 - You're Kidding! Part 1: Deceptive Diagnosis?
When all was said and done, about 0.1% (1 in 1,000) people on Earth became infected with the 'serious' version of the Swine flu virus (a.k.a. 'failflu') during the 2009 Swine flu hysteria.
Suppose, rather than blindly diagnosing anyone with sniffles as 'swine flu infected', the health establishment had developed a test to detect the serious version of the flu with 99% accuracy. That is, the outcome of the test would be correct 99% of the time for both positives and negatives.
Also suppose that you had this test conducted. The doctor worriedly informs you that the results came back positive. He concludes that there's a close-to-99% probability that treatment is necessary (by getting Baxter to inject you with some extra-special magic juice).
Assuming that Baxter's extra-special magic juice is the correct treatment, is the doctor's conclusion correct?
The actual answer would depend on the side effects of the treatment. Assuming the side effects of the treatment if I do NOT have the Swine flu are on par with the risks if I do have the swine flu, treatment would be inadvisable. Out of a random 1000 people, nine would test false positive and only one would be a true positive test. Is that what you are asking?
Also - I am "out" for #40. I tried to figure it out but could not so I looked it up.
Virgil Syonid Message #551 - 06/30/10 04:38 PM
so I looked it up
I wasn't aware that a solution was posted anywhere. You seem to be a whiz at finding hidden solutions.
Is that what you are asking?
Assume there are minimal risks associated with the treatment. The question is more along the lines of: Is the doctor's assessment of your likelihood of being infected accurate?
Gameshow Message #552 - 06/30/10 04:38 PM
darn it, I forgot the lingo (since I haven't seen the chessboard teasers in a while, and I'm too lazy to go back looking for the lingo that was provided earlier )
Here goes,
Lower white knight checks king by moving in front of upper white knight. Two scenarios are then allowed. The black pawn can take the white knight, or the black king can move one space to the left.
Either way, White rook takes black rook and checkmate.
Post by Virgil Showlion on Dec 23, 2010 1:55:48 GMT -5
tall_guy Message #553 - 07/01/10 02:39 AM
I'm leaving problem 40 'open' for now, and posting another hint later tonight.
How's this for a hint?
There are many steps involved in getting the correct answer.
Virgil Syonid Message #554 - 07/01/10 03:06 AM
Still no brave, beautiful souls to have tackled the prize problem (Problem 40 - Carpet Diem @ post #530) ...save for colleenz, whose regrettable compulsion to disqualify herself by looking up solutions has now cost her a third chance at brainteasery glory.
In light of this, EE'ers are offered the following two MASSIVE hints to assist in their endeavours:
The two pieces of rug that result from the can be fit together into a 10' x 10' square without any changes in orientation. That is, you do not need to rotate either piece to get the two pieces to fit together.
The cut passes through the dotted line in the following figure:
Brainteasery glory is calling you!
Yes YOU!
Virgil Syonid Message #555 - 07/01/10 03:08 AM
(Solution to Problem 41)
Colleenz kinda... sorta... suggests the solution in #550: the doctor is grossly mistaken in his assessment.
First the mathematical proof, which is a simple application of Bayes' rule.
Let I refer to the event 'infection reported', H refer to the event 'no infection reported', I refer to the event 'individual is infected', and H refer to the event 'individual is healthy'.
We are interested in determining the probability of an individual being infected if an infection is reported. This is given by:
P(I|I) = P(I|I)P(I) / P(I)
where
P(I) = P(I|I)P(I) + P(I|H)P(H)
Plugging in our numbers, we find:
P(I|I) = 99 / (99 + 999) ~= 9.02%
Hence, there is a mere 9% chance that you are infected even if the 99%-accurate test returns positive.
The less-technical, more intuitive reason for this is also hinted-at by colleenz: the number of false positives (999 per 100,000 individuals) is more than ten times as great as the number of true positives (99 per 100,000 individuals). Hence you're far more likely to be among the group that received a false positive.
Virgil Syonid Message #556 - 07/01/10 03:10 AM
Problem 42 - You're Kidding! Part 2: The Shortest Path to Victory
Suppose two passenger jets take off from Peason International Airport in Toronto. One of the jets is flying due south, presumably carrying the next beaver battalion to 'deal with' the insane, castoricidal SBS. The other jet is flying due east, carrying diplomats who hope to enlist the help of allied beavers in Europe.
Both jets leave at exactly the same time, maintain precisely the same airspeed, and fly at precisely the same altitude.
After both jets have been in the air for one hour exactly, which jet is closer to Pearson International Airport?
I'm going to take a stab and say the Plane flying due south is closer. I figure since the earth rotates from east to west, the plane flying east got more distance covered because it flew east.
-gameshow
whiskmav Message #560 - 07/01/10 10:39 PM
Problem 42
The plane flying due east is closer to its original starting point. Headwind has kept it from flying as far as the plane heading due south.
Post by Virgil Showlion on Dec 23, 2010 1:56:48 GMT -5
rovo Message #561 - 07/01/10 11:07 PM
I'm going to discount the headwinds since Virgil didn't mention anything about them. I'm going with the inverse of Gameshow and say the plane heading east is closer because the earth's rotation is trying to catch the plane. Also the plane traveling south would be skewed to the west as the earth rotates making it further from the origin than just heading south. Touchy problem. Do we assume winds, boundary layer action, or just theoretical stationary atmosphere, and if staionary, then stationary to what, the earth or the sun?
SlowbutSure Message #562 - 07/02/10 12:03 AM
Y'all are all wrong because the beavers would need to head west, not due south, to try to find me.
Some questions for you Virgil: don't the jet packs don't work anymore?; and what does castoricidal mean? I'm wondering if I should add that to my resume.
GeenaMercile Message #563 - 07/02/10 12:40 AM
Spoiler..... Maybe
Okay so I have a question about 42, how are we measuring the distance for the planes by the ground they have covered, such as if we dropped a line from the plane to the ground and measured that point to the airport, or by an imaginary string attached to the plane to starting place and the distance of that string. If we are measuring the ground distance I'm going with the plane heading south being closer.
Both planes leave the airport but because of the curve of the earth the plane heading south to maintain the same altitude the plane heading south would have to fly at at an angle that is not 180 (sorry I don't know what the angle is for the equatorial bulge), while the plane heading east could could just fly at 180 angel. If each planes has an airspeed of 1000 miles and lets say it took each plane 10 mins and 166 miles to reach the altitude they were traveling at, that leaves each plane 833 miles left to travel. The plane heading east can now travel at a 180 degree parallel to the ground and cover 833 miles of ground. Plane heading south, lets say because of the bulge has to fly at a 2 degree angle. Using good old A squared + b squared= c squared and since the right angle would be the line for the plane to the ground, then we know that the 833 miles the plane will travel must be c squared. doesn't matter if you want to call the leg for the ground covered A or B, both must be less then C, so the ground distance that the south bound plane traveled must be less then 833, so the plane heading south is closer.
Okay so that is what I came home with from my drive Now I need to look for flaws in my logic and see if I change my mind.
GeenaMercile Message #564 - 07/02/10 12:45 AM
Name your charity, Ms. Mercile!
Oh wow this was a charity one.... I should choose something like planting trees or save the forest considering the amount of graph paper I used to solve it. I'm going to go with your local wild life rescue or nature preserve.
Post by Virgil Showlion on Dec 23, 2010 1:57:39 GMT -5
tall_guy Message #565 - 07/02/10 02:48 AM
Name your charity, Ms. Mercile!
You know, Virgil, if I thought you really wanted to give the money away I would have posted the solution instead of just a hint....
How's this for a hint?
There are many steps involved in getting the correct answer.
Steps = Many sequential cuts. Steps = Stairsteps. Get it?
I should choose something like planting trees or save the forest considering the amount of graph paper I used to solve it.
I copied the image into Paint and filled in the spaces with color. Easier to restart AND didn't kill any trees....
GeenaMercile Message #566 - 07/02/10 03:33 AM
I copied the image into Paint and filled in the spaces with color. Easier to restart AND didn't kill any trees..
awww but it is so much better to play with the manipulative in your hands instead of just looking at a screen.
tall_guy Message #567 - 07/02/10 03:55 AM
awww but it is so much better to play with the manipulative in your hands instead of just looking at a screen.
Depends on the subject, doesn't it?
GeenaMercile Message #568 - 07/02/10 04:09 AM
Nope, can't really think of a time I would rather be looking at the screen as long as I have the know how, skill, training and talent to handle it in hand. You know as long as there aren't any harmful consequences of trying it in hand I think I would still rather try it in hand then on the screen. Now if you want to see how I fly a plane, lets keep it on screen.
And speaking of planes are you going with the east or south plane.
Post by Virgil Showlion on Dec 23, 2010 1:58:10 GMT -5
Virgil Syonid Message #569 - 07/02/10 06:04 AM
I figure since the earth rotates from east to west, the plane flying east got more distance covered because it flew east.
Interesting. But although the airport is not a static reference, its 'current' position is the most intuitive choice for determining the relative position of the jets.
For example, if you drive east for 100 miles, you are '100 miles away' from your point of origin. The fact that Earth has rotated during this period of time is generally considered irrelevant (since your point of origin has rotated by precisely the same amount).
If we were to assume that the Earth was a stationary rotating ball and the reference for calculating distance was 'the location of the airport at time zero', your argument would be absolutely correct.
Headwind has kept it from flying as far as the plane heading due south.
A worthy observation, but the problem statement points out that the planes maintain precisely the same airspeed. Prevailing headwinds are not a factor.
Do we assume winds, boundary layer action, or just theoretical stationary atmosphere, and if staionary, then stationary to what
You forgot relativity.
No, good puzzlers, I do not require you to pull the problem into Minkowski space and figure out arclengths on a 4-manifold.
Earth is the reference. Relativity is ignored. We can (without loss of generality) assume:
the airport is stationary
the atmosphere is stationary
no celestial body except the Earth is relevant
Both planes leave the airport but because of the curve of the earth the plane ... (sorry I don't know what the angle is for the equatorial bulge), while the plane heading east could could just fly at 180 angel.
This... might... be close to the right explanation, depending on what you mean by 'equatorial bulge'. If you're referring to the eccentricity of the Earth, it's something like 0.017. For all intents and purposes, we can consider Earth to be a perfect sphere.
You seem to have derived an incorrect answer, however.
See the solution posted below.
Steps = Many sequential cuts. Steps = Stairsteps. Get it?
I missed it.
Geena's charity got the cash. Their homepage says they're using it to save snowy owls.
You get the 'runner up' prize: a free "swap out" coupon for rovo's "Stock Pick of the Month" game over in MT. It lets you swap your pick with somebody else's, one time only, anytime during the month. Hence your TSLA -35.61% pick becomes somebody else's problem, and their BGZ +15.58% pick moves you straight to the top of the list.
I'm going to go with your local wild life rescue or nature preserve.
[Virgil], your donation is now complete. Confirmation number: 8W7-------------W.
An email with your donation details has been sent to [your email] and you can print your donation receipt.
Donation Amount: 100.00 CAD
Donations Coordinator Contact Information Toronto Wildlife Centre info@torontowildlifecentr
Virgil Syonid Message #570 - 07/02/10 06:11 AM
(Solution to Problem 42)
Excellent participation in this one, and a lot of brainpower being showcased.
Rovo has the correct answer, but for the wrong reason. I suspect that Ms. Mercile has the correct reasoning (her musings are a bit unclear ) but does not reach the same correct conclusion as rovo.
First, a mathematical fact: the shortest path connecting two points on the surface of a sphere is an arc on a circle that:
has its center at the center of the sphere
passes through the two points
This is called a 'great circle'.
A jet flying south is flying along an arc on a great circle. (The meridians are just 24 great circles that pass through the north and south poles of the planet.)
Hence the shortest path connecting the south jet and the airport is exactly the path it has just flown along.
The east-west parallels are not great circles. Only the equator is a great circle, since it's the only parallel that passes through the center of the Earth. Since the eastbound plane is flying along a parallel (due east), its path is not an arc on a great circle. Therefore, a shorter path is guaranteed to exist that connects the jet (point 1) with the airport (point 2). (If you want to prove this to yourself, blow up a balloon, mark north and south poles, experiment, and prove it to yourself!)
We know that the length of both paths (both arcs) is the identical because the planes have maintained precisely the same altitude and airspeed. Call the common length of the paths x:
There is no path from the south plane to the airport with a distance less than x.
There is a path from the east plane to the airport with a distance less than x.
Hence, the east plane is closer to the airport than the south plane.
Note that the same argument holds if you consider 'distance' to be the length of an invisible string from a jet to the airport, but the solution is harder to prove in this case.
Also note that this is why the flight paths across the Northern US [] 'bulge' into Canada rather than running along straight lines on a map.
Virgil Syonid Message #571 - 07/02/10 06:14 AM
Problem 43 - You're Kidding! Part 3: Tying Up the World
The circumference of the Earth around the equator is about 25,000 miles.
Suppose you managed to wrap a piece of string around the equator (let's assume the Earth is a perfectly smooth sphere).
If you wanted to raise the whole string one foot off the ground, about how much would you have to extend the length of the string?
a) about 6 feet b) about 600 feet c) about 6 miles d) about 60 miles e) about 600 miles
tall_guy Message #572 - 07/02/10 06:54 AM
You get the 'runner up' prize: a free "swap out" coupon for rovo's "Stock Pick of the Month" game over in MT. It lets you swap your pick with somebody else's, one time only, anytime during the month.
Unfortunately, I don't play that game. Maybe we can compromise on a substitute prize. Perhaps your oath of eternal fealty would suffice?
Yes, I think that would do nicely. And best of all, there would be no tangible cost whatsoever.
Post by Virgil Showlion on Dec 23, 2010 1:58:40 GMT -5
tall_guy Message #573 - 07/02/10 07:12 AM
SPOILER
If you wanted to raise the whole string one foot off the ground, about how much would you have to extend the length of the string?
Slightly over six feet. The circumference of a circle is pi(d), where d = the diameter of the circle. To increase the diameter by a total of two feet (one foot on each side) the calculation becomes pi(d+2). Circumference of the new circle is then pi(d) + pi(2). Because pi(d) is the same in both equations, the increase is pi(2), or roughly 6.28 feet.
Now, if you wrapped a piece of string around a basketball, and then wanted to raise the whole string one foot above the surface, how much would you have to extend the length of the string?
GeenaMercile Message #574 - 07/02/10 11:54 AM
Rovos game was fun when I had the time, but it required more computer time. On the other hand I have pulled a few of these problems to share with my summer camp group. So I can justify my time on here as research.
Yea I did kind of jumble my thoughts together with the last one I blame it on the thrill of seeing TG again
whiskmav Message #575 - 07/02/10 05:00 PM
Hence, the east plane is closer to the airport than the south plane.
Hurray! I was right anyway.
whiskmav Message #576 - 07/02/10 05:02 PM
# 546
Gameshow! Way to do it.
For all of you chessophiles it goes....
1. Ng6 + Black has 3 possible moves Kg8 / hxg6 / Rxg6
Post by Virgil Showlion on Dec 23, 2010 1:59:31 GMT -5
whiskmav Message #577 - 07/02/10 05:03 PM
So, It's going to be a long weekend. In order to keep you occupied I give you.....
White to play and mate in 5 moves
Now let's use some of that American ingenuity!
Virgil Syonid Message #578 - 07/02/10 05:26 PM
Perhaps your oath of eternal fealty would suffice?
Hm.
You know you're on the Everything Else board when: you proposition a poster into pledging 100% of their labour to your service, and assume the commitment will incur 'no tangible cost whatsoever'.
I'll just call you m'lord from now on.
Virgil Syonid Message #579 - 07/02/10 06:04 PM
OK..
Well, my 30 minutes are up. I can't figure out #577 for now. That darn king always has an 'out'.
Virgil Syonid Message #580 - 07/02/10 06:22 PM
I just looked up the solution... and discovered that knights can pass over other pieces!
Post by Virgil Showlion on Dec 23, 2010 2:00:01 GMT -5
whiskmav Message #581 - 07/02/10 07:12 PM
and discovered that knights can pass over other pieces!
Who knew!
Virgil, your youthful innocence makes me long for simpler days.
Virgil Syonid Message #582 - 07/05/10 08:26 PM
(Solution to Problem 43)
Tall_Guy gives the correct answer in post #573.
Virgil Syonid Message #583 - 07/05/10 08:29 PM
Problem 44: Oh, The Irony!
Astute EE'ers may uncover some ironic truths in the following questions. How many can you identify?:
Why is the weight of a 'chance' ironic?
Why is salt (sodium chloride) an ironic compound?
Why are the Spanish Inquisition, the Iraq war, and abortion ironic?
Why are sacrament, host, and chalice ironic words?
Why is 'Google' an ironic name for a universal source of information?
Why is brainfreeze ironic?
Why is the 'Daddy Longlegs' spider ironic?
What is ironic about the world's longest recorded sniper kill and the song "Rockafella Skank" by Fatboy Slim?
Mojo the Awkward Message #584 - 07/06/10 04:29 AM
Interesting, Virgil. As a connoisseur of the obscure, I found these challenging. Only the last two struck any sort of chord whatsoever, although I note in passing that sodium chloride is an ionic compound as well as (apparently) an ironic one. I suspected wordplay along the lines of irony meaning "a bit like iron", but neither ferrous nor ferric chloride have anything in common with good old NaCl that this correspondent could divine at such a late hour.
I observe that "Daddy Long-Legs" is both a common nickname for various genera of Harvestman spider and for the Crane fly - it may be that a nickname common to spider and fly constitutes an irony, although I think even La Morissette would purse her lips doubtfully at that.
Although I have determined no common irony between the longest sniper kill and the Fatboy Slim track, I do know that the latter record earned poor Norman Cook no royalties at all, as he was obliged to give up quarter-shares in the royalties to the four artists he sampled on the track; and that the former record was broken in 2002 after a 35-year wait by a Canadian, Master Corporal Aaron Perry, and yet held for only a few days before another soldier in his own unit, Corporal Rob Furlong, took the title from him. It occurs to me to speculate that the fact they are both records, in different senses, may yield a further irony, but it is beyond my grasp at the time of this writing.
Post by Virgil Showlion on Dec 23, 2010 2:00:31 GMT -5
Virgil Syonid Message #585 - 07/08/10 02:36 AM
(Solution to Problem 44)
Only one response!?
Well, at least Mojo had some fun--and came up with some creative answers. The 'correct' answers, and some comments on Mojo's, are as follows:
...the irony being that a "fat chance" and a "thin chance" are precisely the same thing.
...the irony being that although salt (sodium chloride) is found in virtually all foods today, it is composed of sodium and chlorine--two elements which are toxic to humans in their elemental form. (Although the pun on "iron"ic was clever and earns you 5 Virgil points. )
...the irony being that the Spanish inquisition killed (est.) 5,000-15,000 people over 500 years, the Iraq war killed (est.) 150,000-800,000 people over 7 years, and (legal) abortion kills 1,300,000 babies* every year in the US, and yet most Americans rank these three injustices from most to least severe.
*Note: You may exclude this statistic if you believe an human fetus magically transforms into a human baby upon reaching the third trimester.
...the irony being that all three words are perfectly acceptable in English, but are considered profanity in Quebecois.
...the irony being that the name was chosen when Larry Page, pressed for time and lacking a handy information resource to check his spelling, supplied "Google" as a misspelling of "Googol" as the domain name for his fledgling search engine.
...the irony being that the freezing has nothing to do with the brain. Brainfreeze occurs when extreme cold is introduced into the lower esophagus. Pain in this area of the body is "referred" to the forehead.
...the irony being that, as Mojo indicates, "Daddy Longlegs" (which nearly always refers to the Crane Fly or the Harvestman) isn't actually a spider.
...the irony being that the lyrics in "Rockafella Skank" are so repetitive that more than half of them (60%) are uttered with greater frequency than 0.33 Hertz--once every three seconds--on average ...the amount of time it took Craig Harrison's record-breaking bullet to reach its target in 2009. In this respect, the words of the song are delivered faster than bullets.
I do know that the latter record earned poor Norman Cook no royalties at all, as he was obliged to give up quarter-shares in the royalties to the four artists he sampled on the track
That is ironic.
Or at least... halfway to being so.
True irony would be five artists sampled on the track.
Virgil Syonid Message #586 - 07/08/10 02:49 AM
Problem 45 - You Don't Know Math! Part 1 - My Special Number
I am thinking of a special number, x. This special number is not negative.
When I raise x to itself: x^x, I get the number 0.20788.
What number do I get when I raise x to the fourth power (e.g. x^4 = x · x · x · x)?
MN-Investor Message #587 - 07/08/10 04:10 AM
SPOILER (or hint?) (I'm new at this)
I haven't read this thread until tonight. How acceptable is it to google for hints? I googled 0.20788 and power and that gave me the information necessary to answer the problem. Should I post what I think the answer is or is googling for help cheating and I should just shut up?
Virgil Syonid Message #588 - 07/08/10 09:04 AM
I googled 0.20788 and power and that gave me the information necessary to answer the problem.
Darn Google knows everything.
You're certainly welcome to post the solution. All I ask is that you prefix any post with the answer in it with