bonanova

Yup. This word occurred to me when I wuz a kid and before I knew the meaning of the word. I was surprised at the similarity of the meaning to the words I made by spelling it backwards. Anyone know another one like it? Nice going.

Correct. @comperr, that might be correct, but we cant know until we inspect an object from one of the boxes. which box should be drawn from, and how do we reason from what we find to find the correct labeling?

The cards in a deck show either a circle or a square on their faces and have backs that are either red or green. Four cards are dealt. Two are face down, showing red and green; two are face up, showing a circle and a square, thus: [card 1] RED [card 2] GREEN [card 3] circle [card 4] square Someone asks: Of those four cards, does every RED one have a square on the other side? How many cards must be turned over to gain enough information to answer the question? Which ones?

Three boxes are all labeled incorrectly, and you must get the labels right. The labels on the boxes read as follows: [box 1] nails [box 2] screws [box 3] nails and screws To gain the information you need to move the labels to the correct boxes, you may remove a single item from one of the boxes. You may not look into the boxes, nor pick them up and shake them, etc. Can this be done? If so, how? If not, why not? [Edit to add solution.] [Edit again to explain.]

OK here's another clue. Read backwards, the original word becomes 3 words.

I got my bottle of the stuff on e-Bay, and they forgot to mention it.

Yup, and this: how far N E W and S can you go on earth?

Thanks UR, I wuz offline for a couple days..

I assume you are asking for a distinction between the two. To my mind an argument is making a case for a way of thinking, or to establish a point of view. As attorneys argue cases in court. In that sense an argument is much the same as a debate. Debaters need not personally hold the positions they argue. Nor need an attorney. S/he is hired to speak in favor of a point of view In a dispute there is a clash of two opposing held views. Here the protagonists actually hold the views, and they may take action up to and including crimes of violence or as nations sometimes do, wage war. An argument can be theoretical [except when it involves my wife ] ; a dispute is never just theoretical.

Well like many things proof is less significant than is our agreement with regard to premises. 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....

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. 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 2-boy families from the population of 2-children families and then look at the fraction of 2-girl 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 2-boy 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. 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, un-advertised feature of making one's retina sensitive to those wavelengths. Kind of like the IR switch on the newer camcorders and the so-called "x-ray 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!

Maybe not. But it is a brain teaser of sorts. Let's wait for the first-posted answer to find out.

The probability 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 2nd-birthed 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 2nd-birthed 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! 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! A 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! 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?

I'm all for that. Do you happen to have mum's phone number?

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. 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. Men wear shades at the beach for more reasons than just protecting their retinas from uv-radiation. 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 2-1. 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.