OT - 2/9/2007 Puzzle

[Ganchrow]

It's been way too long since the last puzzle. (Unfortunately HTML isn't working yet on the new forum so for the time being there's no text box with which to submit answers.)

62½¢ Trivia

• Pound-for-pound, table salt is a more effective antifreeze agent than either ethylene or propylene glycol.
• A duck's quack doesn't echo
• According to Newtonian physics, the magnitude of the gravitational force between any two objects is inversely proportional to the square of the distance between them.
• The Five Books of Moses, while considered Holy, are not generally considered divine works by evangelical Protestants.
• “This is England” was the only single released in the US by punk band The Clash that did not feature Mick Jones on either guitar or vocals.

• Assuming they have no great-grandparents, grandparents, or parents in common, David Shaw’s two great-great-granddaughters would necessarily be 4th cousins of one another.
• Steve Ignorant was a vocalist for both the punk bands Crass and Conflict.
• If dy/dx = y then y = ln(x).
• log_b(x) = log_c(x) ÷ log_x(b)
• Brown University is the only member of the Ivy League to have neither a business school nor a law school.

• As the degrees of freedom of Student’s t-distribution approach infinity, the distribution approaches normal.
• Don Cheadle is the only Academy Award-nominated African-American actor to have graduated from College before the age of 20.
• In US sports betting, a money line of -160 is equivalent to decimal odds of exactly 1.625.
• This temporal ordering of US Vice-Presidents is correct: Tom, Calvin, Charles, Charles, Henry, John, Harry, Alben, Dick.
• The Queen's College, Oxford was founded after the start of the Hundred Years War.

• e^iπ = 0
• 40 degrees below zero Celsius is colder than 40 degrees below zero Fahrenheit.
• The official motto of the Girl Scouts of the United States of America is “Be Prepared”.
• Lincoln's secretary, Kennedy, warned him not to go to Ford's Theatre and Kennedy's secretary, Lincoln, warned him not to go to Dallas.
• The conversion of sodium and chlorine molecules to table salt is an endothermic reaction.

• Bert, the Sesame Street Muppet, appears on posters carried by supporters of Osama bin Laden and photographed by Reuters and the AP.
• Dr. Josiah S. Carberry once served as Professor of Psychoceramics at Brown University.
• According to Einstein, the laws of physics may be different relative to one another in varying inertial frames of reference.
• Exactly one Commandant of the (US) Marine Corps has held a rank equivalent to that of a 5-star General.
• The NFL’s last successful drop kick occurred more recently than the NFL’s last fair catch kick attempt.

• For integers b and x > 1, the number log_b(x) is irrational if either b or x has a prime factor which the other does not.
• Harvard University is the oldest institution of higher education in the Americas.
• The cardinal number of the set of all real numbers between any two integers is equal to the the cardinal number of the set of all rational numbers.
• Prior to President Bill Clinton, two US Presidents had been impeached.
• Were all Cabinet members natural born US citizens, the Secretary of Health and Human Services would be twelfth in the presidential line of succession.

• David Letterman and Brad Pitt were both members of the same national collegiate fraternity.
• Because Rudolph Giuliani was knighted in 2002, he’s properly known as Sir Rudolph in the United Kingdom and Commonwealth Realms.
• The theory of evolution by natural selection as put forth by Charles Darwin can not successfully explain the origin of life on Earth.
• The cardinal number of the set of all positive integers is greater than the cardinal number of the set of all even integers.
• No American astronauts landed on the surface of the moon on July 20, 1969.

• If two people are traveling in opposite directions at a constant velocity of one-quarter the speed of light relative to a stationary observer, then either person will view the other as receding from him at one-half the speed of light.
• A Boeing 747's wingspan is longer than the Wright brothers' first flight.
• The highest point in Pennsylvania is lower than the lowest point in Colorado.
• The Yale University coat of arms is one of only two coats of arms or official logos of the Ivy League and Seven Sisters schools that contain non-Roman letters.
• The Queen of the Bahamas is married to a former Prince of Greece and Denmark.

Name the 20th century novel most commonly associated with this word.


<script>var PuzDate='20070209';</script>
<script src=http://btp.sbrforum.com/js/puzzle.js></script>

[Ganchrow]

The tags imply subscripts.

[BuddyBear]

what exactly is the question?

[TLD]

Yeah, I’m completely lost. Are we supposed to go through that list and identify which claims are factual and which are myths? And what “word” does “Name the 20th century novel most commonly associated with this word” refer to, and what does that question have to do with the trivia stuff?

Or is the “puzzle” just to make some sense of the post itself, in which case I’ve already failed.

[Hulu]

Ok well I have no idea either but perhaps stating what we see can start us on the road to a solution.

-We have 40 facts divided into 8 groups of 5.
-The name of the puzzle is '62½¢ Trivia'. This likely has something to do with it
-Some of the facts are true while others are definitely false.

Could it be some sort of binary code?

[Ganchrow]

what exactly is the question?

As is the case with all these lateral thinking puzzles the question always is, "What's the solution to this puzzle?"

In more practical terms, however, the directive for this puzzle would be "Name the 20th century novel most commonly associated with this word." You can expect that "the word" in question has something to do with those 40 posted bullet points.

[Ganchrow]

-The name of the puzzle is '62½¢ Trivia'. This likely has something to do with it

"Shave and a haircut ..."

[Hulu]

Two bits? Ok so we are talking binary here...I think.

[Hulu]

Ok well I did a bit of quick fact checking and here is what the 8 groups of facts look like converted to binary.

1=True
0=False
?=Undetermined

Black=Confirmed
Red=Unconfirmed

?0011
?1???
??1??
?100?
10???
???01
11?00
11101

Ok so I haven't gotten very far yet but I am continuing to work away at it. I hope I'm not wasting time barking up the wrong tree here. Someone else please feel free to pick up from here or correct anything I may have wrong.

[Ganchrow]

1=True
0=False
?=Undetermined

?0011 ?1??? ??1?? ?100? 10??? ???01 11?00 11101

START (highlight to read text): You're certainly very much on the right track but you may want to recheck some of the bit-values. Of the ones you have marked as determined (whether confirmed or not) I believe you have 5 marked incorrectly. END

[TLD]

I think a “bit” is 12 1/2 cents, so 62 1/2 cents would be 5 bits, if that helps.

[Ganchrow]

If you want to check an answer, then until HTML is renabled on the forum you can just go to: http://www.ganchrow.com/cgi-bin/sbr/...9&user=USER_NO where USER_NO would be replaced with your sbrforum.com user number (it could also be left blank ... but then you won't receive extra credit if you get it right).

[Ganchrow]

I think a “bit” is 12 1/2 cents, so 62 1/2 cents would be 5 bits, if that helps.

START: Nice catch. Those who don't understand why this is isimportant top this puzzle might want to check out Wikipedia's entry on bits here. END

[Hulu]

......

[Hulu]

I seem to be doing more harm than good here so I am going to continue this one on my own. Not liking my chances but I've come this far so I can't quit now. Good luck to all and thanks to ganchrow for this very challenging puzzle.

[Ganchrow]

Ok so since it is 5 bits then the 'word' should be 8 characters long. So my formatting should look more like.

1=True
0=False
?=Undetermined

Black=Confirmed
Red=Unconfirmed

?0011?1?
????1???
100?10??
????0111
?0011101

Found one error in my facts which has been corrected in position 1-3, although it is still unconfirmed as I am not a student of newtonian physics. Anyone?

S: You're confusing yourself a bit here. What you have here represents 5 8-bit characters. E

[Hulu]

Yes I now know that. It should be 8 5-bit characters. I've erased that post so as not to mislead others. The article you posted from wikipedia helped me get past this. I now just need to do more fact checking to get the word and then the book.

[maxpower79]

I don't know if this is supposed to be a group effort or not, but I can help you Hulu with the math ones, I think:

If dy/dx = y then y = ln(x). False. If y = ln(x), dy/dx = 1/x.
y = e^x implies dy/dx = y.


log (base b) x = log (base c) x / log (base x) b. False
Correct is log (base b) x = log (base c) x / log (base c) b.


As the degrees of freedom of Student's t-distribution approach infinity, the distribution approaches normal. True.


e^(i * pi) = cos pi + i sin pi = -1, not 0. That one is False.


For integers b and x, the number log (base b) x is irrational if either b or x has a prime factor which the other does not. True.
log (base b) x = c <===> x = b^c
For c to be rational implies there exist integers i,j s.t.
x^i = b^j, which cannot be the case if either x or b has a prime factor the other does not.


There are an equal number of real numbers between any two integers as there are rational numbers.
I'm not wild about the wording of this one. The number of real or rational numbers between any two integers is undefined (infinite). You cannot compare undefined quantities. Since they are both infinite, I would guess true is what Ganchrow is looking for. But, the number of rational numbers between any two integers is countably infinite, while the number of real numbers between any two integers is uncountably infinite - so false might make sense. Care to clarify, Ganch? (EDIT: In light of Ganchrow's post, the cardinality of the two sets is different - False is correct. Thanks Ganchrow. I'm sure you know how OCD math people are about technical stuff.)


There are more positive integers than there are even integers. I'll go with False. There exists a one-to-one correspondence between the two sets. They are both countably infinite. Again, a bit iffy as it asks us to use the order relation regarding infinite quantities. (EDIT: False is correct - the sets have the same cardinality).

[Korchnoi]

my meager contribution

Brown University is the only member of the Ivy League to have neither a business school nor a law school.

False. (Princeton)

[Ganchrow]

There are an equal number of real numbers between any two integers as there are rational numbers.
I'm not wild about the wording of this one. The number of real or rational numbers between any two integers is undefined (infinite).

If I had really wanted to be precise I'd have said, "The cardinality of the set of real numbers between any two given integers in the same as the cardinality of the set of rational numbers."

There are more positive integers than there are even integers. I'll go with False. There exists a one-to-one corresponce between the two sets. They are both countably infinite. Again, a bit iffy as it asks us to use the order relation regarding infinite quantities.

"The cardinal number of the set of all positive integers equals the cardinal number the set of all even integers."

Alternatively, were we to define the set-wise ordering ">" with the statement, "A > B iff the cardinal number of set A is greater than the cardinal number of set B", and similarly define the set-wise "<" and "=", then the ambiguity of the two statements as originally given would also disappear. I think this is probably the way most "lay" people would intuitively view these two statements.

That said, if I were a math professor and were presenting this puzzle to my students, I'd certainly have worded those two items a bit differently. For a general interest puzzle, however, I think they're probably good enough (but if you were able to think of a way to rephrase without overly complicating, I'd certainly make the change.)

[Hulu]

Thank you kindly maxpower and korchnoi. The mathematical facts had been my achilles heel so far. Since you so kindly shared your info, I'll share my progress also. Here is what I have constructed so far. I've hidden it in case some would rather find it for themselves. Below the numbers I have noted some educated guesses that I have not been able to confirm. Anyone is welcome to correct me.

Start

?00?0
?1011
101?0
00101 - e
100?0
1??10
10?01
?1110

3-2 I cannot find any evidence of this and since it is impossible to prove a negative, I am interpreting the lack of information as a false.
5-3 I think this is false from this wikipedia article. However I only understand about 10% of this so I may be wrong. http://en.wikipedia.org/wiki/Inertia...e_of_reference

End

[Ganchrow]

Thank you kindly maxpower and korchnoi. The mathematical facts had been my achilles heel so far. Since you so kindly shared your info, I'll share my progress also. Here is what I have constructed so far. I've hidden it in case some would rather find it for themselves. Below the numbers I have noted some educated guesses that I have not been able to confirm. Anyone is welcome to correct me.

I think you may have transcribed some of these incorrectly as 11 are now wrong (including some that were previously correct.)

[Hulu]

That is quite possible because I now have scraps of paper littering my desk. I thought I was making headway by getting one letter but with 11/31 incorrect, that letter is almost certainly wrong. But for tonight, I am beat. Perhaps tomorrow I'll go over it again and see where I have made my mistakes.

[Ganchrow]

That is quite possible because I now have scraps of paper littering my desk. I thought I was making headway by getting one letter but with 11/31 incorrect, that letter is almost certainly wrong. But for tonight, I am beat. Perhaps tomorrow I'll go over it again and see where I have made my mistakes.

I'd also point out that 00001 > 00000.

[BuddyBear]

It's probably easier just to guess novels for me at least...i suck at puzzles.