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Posts posted by bonanova


In the first case we're talking about accelerating something that has nonzero mass to the speed of light. It's not a simple matter [no pun intended], since mass increases without bound as that speed is approached. Thus increasing the required accelerating force without bound.if Einstien says that it take an infinite amount of energy to reach the speed of lighthow can (energy equals matter times the speed of light squared or E=MC2) be true
In the second case, he asserts the equivalence of mass and energy. In a nuclear reaction where the final particles are less massive than the initial ones, energy is given off. The amount of that energy is given by the decrease in mass multiplied by the square of the speed of light.
Are you asking whether these statements form a contradiction? They don't because [1] they concern different things, and [2] ... uh ... oh yah, Einstein is way smarter than either of us, and he wouldn't say contradictory things.

In the literature, scholars say the answer can be 50%.
The way they arrive at 50% involves how the couple in question is chosen from the set of all couples with two children.
And Yes, Virginia, it really makes a difference.
The "1/3" proponents in this thread [i'm one of them, given the wording skate gave us] interpret the question
in a manner that permits us to simply exclude the 2boy families from the population of 2children families
and then look at the fraction of 2girl families in that smaller set. With that approach, the answer is 1/3.
The 50% proponents argue that the problem might be interpreted in a way that allows us to conclude
that we have been given knowledge of one particular child. That seems a very subtle difference,
but it does change the sample space, and it does change the answer.
And the endless confusion in the debate on these pages is that it is not recognized that the debate
is about the information we feel that we are permitted to assume, and not about the logic.
OK, in some posts the logic was really silly.
But that aside,
Here's how the 50% proponents rephrase the riddle:
More fairly, how the 50% proponents claim the riddle can validly be rephrased:
You meet a woman on the street who is with her daughter.
You ask, how many siblings does your daughter have?
She says, one.
She doesn't give you the sibling's gender.
OK, they say, here is a random parent with two children, and you know only that [this particular] one of them is a girl.
What are the chances the other is a girl? In this case, the answer is 50%.
That subtle difference in choosing the sample space changes the answer. Note that it does not
include mothers for whom it is known only that the gender of the child not present is female.
Now for all of you 50% people who have jumped up on the table and begun to dance, please note:
I don't disagree, and [gulp] speaking for Martini and others [always dangerous to do]
none of the 1/3 proponents would disagree with this, either.
We only disagree that the problem as stated by skate cannot validly be restated this way.
To summarize ...
The serious debate on this question concerns [only] how the sample space is selected.
You have to look at the precise wording of the posed question in order to set up the categories.
Here's how one scholar distinguishes the two cases:
You meet a woman and ask how many children she has, and she replies "two." You ask if she has any girls, and she replies "yes."
[this is the case of the general population minus the 2boy families.]
After this brief conversation, you know that the woman has exactly two children, at least one of whom is a girl.
When the question is interpreted this way, the probability that both of her children are girls is 1/3.
You meet a woman and her daughter. You ask the woman how many children she has, and she replies "two."
[This is the case where the gender of one specific child is known to be female.]
So now you know that this woman has exactly two children, at least one of whom is a girl.
When the question is interpreted this way, the probability that both of her children are girls is 1/2.
If I may speak for the "1/3" contingent in this thread, we hold the 1/3 answer because ...
we assert that the problem as stated by skate precludes being recast in this latter form.

Basically, yup.heat sensor?The invisibility potion renders people invisible to [duh] visible light  say 4000  7000 Angstroms.
However, for longer wavelengths, say 8000  12000 A, it leaves people, and their retinas, quite opaque.
The potion has the additional, unadvertised feature of making one's retina sensitive to those wavelengths.
Kind of like the IR switch on the newer camcorders and the socalled "xray vision" pics that some people look at on the Web.
Donna and Theresa were "hot" enough [ah, that was a clue] to emit generous amounts of energy in those wavelengths.
I have to say that the girls weren't as attractive viewed in shades of gray and without visible suntans.
But ... Donna ... well, she made up for that. *wink*

Heh heh, you scallywag!we can overpower him... 
Maybe not. But it is a brain teaser of sorts.does this count as a riddle?Let's wait for the firstposted answer to find out.

The probability of a child being a boy or a girl will always be 50%,I still do not understand your reasoning.No matter what, the chances of a child being a boy or a girl will always be 50%.
regardless of the gender of any previously born siblings. Agreed.
But in the question being asked the two children are already born,
and their family falls into a certain class.
We are told that one of the children is a girl.
Think about this for a moment.
Some families with two children don't have any girls, much less two girls.
So we're not talking about just any family.
Then think about the probability of the child that is said to be a girl being either a boy or a girl.
Clearly, it's not 50%.
So, "50% must be the answer" only applies when the scales are not tipped.
Let's see why and how the scales actually are tipped in this case.
To see this, let's consider a case where the scales are not tipped.
"A couple has a girl and then they have a 2nd child.
What is the probability the 2nd child will be a girl?"
The answer is 50%.
So, to see how our answer might be different from 50%,
let's see how the this question differs from the one actually being posed.
Consider:
Families with two children fall into the 4 equally probable classes of
1 boy then 1 boy [25%]
1 boy then 1 girl [25%]
1 girl then 1 boy [25%]
1 girl then 1 girl [25%]
As we just saw, the probability that the 2ndbirthed child is a girl is 50%.
Those classes are 1 boy then 1 girl [25%] and 1 girl then 1 girl [25%].
But the question does not ask the probability for the 2ndbirthed child.
It asks the probability for the other child, given that one of the two children is a girl.
Given that one of the children is a girl eliminates one of the four classes of families above.
We're now looking at the set of families that have two children, one of which is a girl.
We can no longer consider the case of 1 boy then 1 boy.
And that tips the scales.
We now are considering only three equally likely classes of families:
1 boy then 1 boy? Nope, [0%]. These families have been asked to leave the building, so to speak.
1 boy then 1 girl? Yes. [33%]
1 girl then 1 boy? Yes. [33%]
1 girl then 1 girl? Yes. [33%].
Now look at these classes, and ask: given that one of the children is a girl,
what are the chances that the other one is a girl?
Take a minute to be sure of the conditions of the question,
and of the equal probabilities of the classes,
then find the classes that provide a correct answer.

Bravo regardless. you certainly engaged a number of us for a while!I must first apologize profusely for not proof reading my puzzle before submitting it. As such I've frustrated and annoyed you all. The method proposed by bonanova and unreality WERE correct, it was just that I messed things up by not proof reading.As far as proofreading goes, it's difficult at best, and yours was
more challenging than most.
I was about to post the following, but it probably falls into the proofreading
category, as well, and [obviously now] is not a step toward the solution.
Line [12I] has 25 words  probably from shortening "that is" to "that's"
Line [17Q] "Haikus ..." has 27 words.
Line [18R] "So they ..." has just 25.
You must have had fun putting this one together.
Hope you do more.

Great observation!each of the 26 line breaks, are made up of 26 wordsA 26 x 26 array of words.
Unfortunately A's are not missing from the 1st column, etc.
But this gives us something new to look at.
Nice job.

You got it. Nice going!Now Bananova can explain how / why we always come up with a digit total of 18, or is this just coincidence?And you resisted the red herring of 0 1 4 and 6 appearing in both cases.
The trick works because of two interesting properties of the number 9.
[1] scrambling a number's digits changes its value by a multiple of 9.
[2] adding the digits of a multiple of 9 gives another multiple of 9.
So the solution is to subtract the sum of the given digits from the next
higher multiple of 9. It just happened to be 18 both times here.
And the prohibition of not crossing out a zero is to distinguish
it from the case of crossing out a 9.
Now, can you prove these two interesting properties?
[1] Start with the simplest case: move a 1 from the units place to the tens place.
You've added 9 to the value: 10  01 = 9.
Move it from the units place to the hundreds place.
you've added 99 to the value: 100  001 = 99.
And so on for moving to any other place in the number = always a multiple of 9.
Move a number other than 1, say 7.
You change the above results by a factor 7, but it's still a multiple of 9:
70  07  63 = 9*7
700  007  693 = 99*7
Pair switching produces sums of multiples of 9.
Scrambling all digits is a series of pair switches.
[2] Work the above backwards:
Start with 9.
Decrease it by 1 and put the 1 in some other place: 18, 108, 1008, etc.
Two things happen. The digits still add to 9;
and, by the above reasoning, the new number differs from 9 by a multiple of 9.
You can create any desired multiple of 9 by successive changes of digit values in this manner.
Thus any multiple of 9 adds digitwise to a multiple of 9.

I'm all for that. Do you happen to have mum's phone number?life is too short.. let's have some fun too .. 
Clue: How do the numbers 6 1 4 0 1 give away that 6 was crossed off?
Another case: 753487  345877 = 407610
this time cross out a 7.
scramble the remaining digits and tell me 6 0 0 1 4.
How do those numbers give away that a 7 was crossed off?

Quite right.how bout we focus on your "palindrome" which of course is not a "palindrome"It's a palindrome only if it reads the same backwards.
And my word doesn't do that.
Instead, when read backwards, it gives a meaning of the word.
Here's a clue: E _ _ _ _ _ O.
Agree, Martini blew the lid off the contranym thing.
For the record my words were sanction, which was in Martini's list,
and resign, which was not.
As in, "After yesterday's game, Jones resigns."
Did Jones get a new contract or did he quit?

They would. Girls always notice when they're being scoped out. Always.However even if the material was completely 'clear' otherwise, like from the inside, if light doesnt get from outside to your eyes you cant see... so maybe cut holes for your eyes? but this of course defeats the purpose, eh. But i dont think they would notice a small eyehole, would they? lolMen wear shades at the beach for more reasons than just protecting their retinas from uvradiation.
So you've established Martini's impossibility argument.
But I claim I did see both Donna and Theresa, and they did not see me.
Here's a clue:
Donna had [by far, really] the better figure, but I couldn't tell who had the better tan.

Geographically.
If the magnetic answer is different, include it for bonus credit.

8
here's why:
Say the fields are 6 acres and 3 acres,
and assume every man works at the same rate.
whole group did 2/3 of the 1st field [4 acres] the first morning.
half the group did the remainder [2 acres] the first afternoon.
It has to be 2/3  1/3 because the worker ratio was 21.
half the group did [again] 2 acres of the 2nd field in first afternoon
leaving 1 acre which required the entire second day for one man to do.
thus each man scythes 1 acre/day.
half the group did 2 acres in 1/2 day [4 acres/day] => 4 men.
whole group did 4 acres in 1/2 day [8 acres/day] => 8 men.
there were 8 men in the group.

OK ...
so the idea is 26  there are 26 LINE BREAKS  well, 25 line breaks;
26 lines of text, each spanning perhaps more than a single sentence.
So we parse by line breaks rather than by periods  alluded to perhaps
by the clue: "show off lipograms, and uses in periods gone.]"
Then there's the clue about Tryphiodorus .. where the 24 Odyssey chronicles
were missing the corresponding greek letter. And in the 9th line, corresponding
to the letter I, he goes out of his way to avoid that letter
by saying is was difficult to express one's own name
instead of the more natural his own name.
But that approach, hoped for by unreality and me, doesn't work:
Lines 4,12, 14 and 20 contain, respectively, d, l, n and t.
Here are the lines, with the number and corresponding letter in parens.
[1a] I've spent the previous hour or so discovering one interesting property concerning linguistics. It's given me much enjoyment while writing the text you're viewing just now.
[2b] Noted as far in the past as 1853, I speak of a unique literary marvel called the lipogram. Let me further enlighten you on this matter.
[3c] Works of Shakespear and even the Bible have been rewriten in lipogram form and there exists a fairy tale entitled Ella Minnow Pea by Mark Dunn.
[4d] It tells the story of a country where certain letters begin to be outlawed . Letters vanish within the story as well as the books' text, simultaneously!
[5e] This is lipogrammation at its top and shows skill from said author. For at points, lipograms prohibit and limit wordflow and linguistic ability a high amount.
[6f] Another humorous example is of a Mr Gottlob Burmann, an eccentric German, 18th century poet who had an obsessive dislike in relation to the letter R.
[7g] He wrote some 130 poems without using the letter once! Not only that but Mr Burmann omitted the letter from his daily conversation for 17 years!
[8h] A strange trait it certainly was, and may seem incredible to you, but to make it more peculiar still: Consider, for a moment Mr Burmanns last name.
[9i] Correct, there's an R there! So how could Mr Burmann express ones own last name? He could not! And so was forced to use a pen!
[10j] Another example still is that of Brandreth, a British lipogrammarian who specializes in rewriting works of Shakespear in lipogram form. He rewrote Othello excluding letter O.
[11k] He rewrote Twelth Night without the letters I and O and Macbeth, excluding both A and E. Most interesting though, was his unique version of Hamlet.
[12l] Which dropped every I. This wasn't a problem for the witty character though, who instead pondered: "To be or not to be, that's the query."
[13m] Finally, consider Tryphiodorus, a poet of ancient Greece who wrote the epic Odyssey which was a chronicle of the adventures of Ulysses. These chronicles totalled 24.
[14n] As you may be aware the Greek alphabet has 24 letters, and for each of the 24 books of Odyssey Tryphiodorus removed the relative Greek character.
[15o] Thus the first tale was written entirely excluding the letter Alpha, the next excluded Beta, Gamma, and such. Indeed this may be the earliest established instance.
[16p] As you can see it requires great skill and attention to detail. In that sense, it is not entirely unlike Haiku, they both have similar restraints.
[17q] Haikus differ by placing a 3 line limit and a further restriction on the number of sounds or syllables on each line, five, seven and five respecitvely.
[18r] So they both have tight limits in place which demand dedication and attention, and the good ones will take much time and skill to complete.
[19s] Anyway, I have veered from the main point which I will now admit. An alternative motive can be found in the creation of the current text.
[20t] Objective number one, I'll reveal, is simply: show off lipograms, and uses in periods gone. My secondary is here for your discovery, in words before you.
[21u] Objective two was to create my own lipogram (of sorts) from the text and sentences on this very page. I've almost completed the task, I hope.
[22v] You see the fairy tale I mentioned earlier inspired me to try something similar, and while it's almost complete, I can't help but stop and reflect.
[23w] On Mr Burnmann. For unlike the others he didn't chose his affliction and so developed his skill as a side effect. Though he's better for it!
[24x] His problem forced him to engage his brain and write within constraints and restrictions. In doing so it created a unique poet and an interesting story.
[25y] Alas, I digress again. Suffice to state that the lipogram is a unique and interesting application of written language (it can be applied to all languages).
[26z] It's been in use for centuries and hides between the words until it suddenly dawns and smacks you in the face. Good luck finding one here.
Now, he said I came close but no cigar a couple times.
That could mean his allusion to the letter manipulation in the fairy tale:
Ella Minnow Pea, where letters are progressively outlawed until finally only
LMNOP [hence the title!] remain in use.
But I don't see a restricted letter set in the author's narrative.
Finally, perhaps we should give attention to his paragraph breaks.
Look at: ... I can't help but stop and reflect.
[new paragraph]
On Mr Burnmann.
What's that all about ... ? certainly an unnatural way to break up a thought.
There are nine paragraphs. Nine doesn't seem significant.
In my first post, I looked at missing letters by paragraph and stopped
after the 3rd because no pattern was apparent.
Still scratching my head.

great list.
one of mine is there, the other is not.
i'll think of a clue or two...

OK, this time I counted '!' and '?' as entence endings. So, I believe the correct count is 48 sentences. I do agree that the third sentence has a 'c' in it. I tried looking for simialr patterns, but did not see any.
I agree with your sentence count.
I got 50 by counting the two ":"'s as sentence parsers  because he began the following clauses with capital letters.
But I think that does not signify a new sentence, technically, and 48 is the correct count.
Another thing i did was look at the paragraph breaks
Paragraph 1  [no a b f q z  4 missing letters]
Paragraph 2  [no z  1 missing letter]
Paragraph 3  [no j q z  3 missing letters]
I gave up on paragraphs after the 3rd.
I think a strong clue is that he said he tried to do something like what was done in the fairy tale,
where letters were progressively outlawed.
That is, a progressive disappearance of letters.
But I didn't see any evidence of that.
I'm actually getting to like this one ...
and I am very interested to see if someone cracks it.

Tried it just now. I will need time to get the hang of it. Thx for the link.

Megamatt asked for a selfcontradictory word [his was "cleave"]
one that has alternative definitions with contradictory meanings.
Cleave can mean to separate or to join. And he asked whether
there were others.
There are at least two other words with contradictory meanings.
They are both common words.
There is also a word whose palindrome [letters in reverse sequence]
is a sort of definition or meaning of the original word.
Now that's strange!
Do you want clues? or do you just want to think about this for a while?

Yah I know about that potion ... I used it, actually, and it turns out that both Donna and Theresa are really hot !!!
Ooops ... given the explanation Martini gave, how could I have seen the girls ... ?

ha ha ha
Didn't notice your post till just now.
Glad someone got it ... *grin*

What are the
Northernmost,
Southernmost,
Easternmost and
Westernmost
states in the US?

My bet is that Forman started out in Alaska ... because
AK is in the US, and it straddles the International Date Line  which itself is not straight. There must be some way that you end up on the other side of it and it's magically yesterday.
Literarily thinking
in New Logic/Math Puzzles
Posted
Most of us can make a valid logical argument from a premise to a conclusion.
We might debate a conclusion, but not because of possibly flawed logic,
rather because we don't share common premises.
Visit the one boy one girl thread for a demonstration of that thought.
My premise:
I would hold that "meaning" in your original question is bound up
with the notion of sharing a thought with you by means of using
words that carry meaning held substantially in common.
That said, my statement would seem to follow: when the commonly
understood word is translated to a concept by you, then its meaning
has achieved significance because it has accomplished something.
And, as I stated above, that doesn't prove my statement, it only
reveals the premise behind it....