Why would it not?
Monty Hall
- Thread starter ebee
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I think you are probably confusing things a bit, since I still think that EFLI was not right in the way he was interpreting and regarding your question.
As you know, I'm not all that happy with this idea of basing one's answer on the fact that there had to be an answer that was independent of hole diameter - but, neverthelss, I regard that as a mathematical approach to the problem.
EFLI, on the other hand, was taking a totally different (incorrect) view - regarding it as a 'trick question', not a mathematical one at all ... thinking that 'the volume of a sphere' (when not explicitly stated as 'the volume of material in the sphere') remain unchanged regardless of any holes (of whatever shape or size) drilled into it. I'm all but certain that such was not what you intended, was it?
Kind Regards, John
That's surely obvious. Men very rarely change their names (hence the reasonable assumption that the question did not relate to some past name of David Cameron - thereby essentially removing tha ambiguity), but women very often do (so either of the ambiguous questions could still be intended).
Kind REgards, John
OK then.
If you take the question to mean "Who was PM in 1950?" the answer would be Clement Attlee.
If you take it to mean "What was the name of the current PM in 1950?" the answer would be Margaret Roberts.
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No, but I fail to see why there is any less ambiguity if one changed the dates to now and 1971....
... because if one knows that it is a 'serious question' ('on Newsnight'), and knows (or is 'all-but-certain') that David Cameron has not changed his name, then one can essentially discount the interpretation of "what was the present Prime Minister's name in 1971", hence almost eliminating the ambiguity - whereas, since the PM was female at the time (and hence pretty likely to have changed her name in the previous 35 years), the same was not true in 1985.
Kind Regards, John
Quite so!Shame the forum doesn't support the necessary font.If I had written 166.7π, someone may well have said that was 'inaccurate'. Similarly if I had written 166.67π, 166.66667π,or even 166.66666666666666666666666666667π - so I thought it 'safest' to put 500/3
Indeed, or some other equivalent which left no doubt as to what you were asking (like the suggestion I posted a page or two back). I'm not quite as daft as you might think, and 'predicted' that someone was going to misinterpret the question in the way that EFLI did - which is why I 'warned' you, immediately after you first posted the question, that 'an increase in clarity' would be desirable.
I suppose so (unless the forum comes to accommodate more fonts!), but that's pretty trivial compared with (1). [FWIW, I'd call it 'recurring', as in "6 recurring", not 'repeating']
Kind Regards, John
I probably should have suggested two other things...
Firstly, that you find a way of explicitly and unambiguously indicating what you mean by the 'length of the hole' being 10cm, to prevent EFLI applying his interpretation which includes the length of the 'imaginery end caps' of the material which has been removed!
Secondly, that, just to be totally sure, you should perhaps make it clear that you wanted a numerical answer - otherwise someone might give you an 'algebraic' answer. For example, they might try a few things 'which felt possible' and come up with an answer such as "the volume of the sphere minus the radius of the hole cubed". That is dimensionally correct and would work in the special/obvious case in which the hole diameter was zero (when the answer obviously has to be equal to the volume of a sphere of 10cm diameter) - so if they were invoking the 'since the question has been asked, there has to be a single answer' approach, they might think (incorrectly) that they had discovered the correct answer (as an expression), which applied with any hole radius...
... In passing, that's one reason why, in a general sense, I regard the 'since the question has been asked, there has to be a single answer' approach to solving a problem as being a bit iffy. If one is allowed an expression, rather than a numerical value, as one's answer, then it is only too easy (as above) to come up with an expression which 'works' in one special case but not in any others. However, I agree that's not an issue if one has asked for a numeric answer.
Kind Regards, John
Isn't that just a special case? What about 4/7?
Maybe times have changed, but I was brought up to call it 'recurring', whether it one one digit, six digits or however many digits that were repeated, with symbolic representation such as:
Kind Regards, John
Like EFI, I also was mixing up the length of the hole with the depth of a drill. John's explanation put me right; like most things, once it is clear, it's hard to see why we saw it incorrectly, but intuitively (I think) I originally thought about how would I make such a real hole and thus was tricking myself in the way I looked at the puzzle. Certainly stating that the measured hole depth was that of the cord parallel to the axis and would (always) be 10cm, would have changed the mental image.
IIRC when I first saw the puzzle there was a diagram like the one I posted, or there was in the answer, so maybe within my minds eye I thought my description was sufficient.
Amyway - a man is paddling a boat upstream. He passes under the first of two bridges one mile apart. As he passes under the second, his hat falls into the river, but he doesn't notice immediately, In fact, he doesn't notice for ten minutes, at which point he turns around and paddles back to retrieve his hat, but doesn't paddle any harder than he had been doing before. He catches up with his hat just as it passes under the first bridge.
How fast is the river flowing?
Amyway - a man is paddling a boat upstream. He passes under the first of two bridges one mile apart. As he passes under the second, his hat falls into the river, but he doesn't notice immediately, In fact, he doesn't notice for ten minutes, at which point he turns around and paddles back to retrieve his hat, but doesn't paddle any harder than he had been doing before. He catches up with his hat just as it passes under the first bridge.
How fast is the river flowing?
Lest some manage to misunderstand the question again, may I suggest that it should be clarified that not only did he not paddle any harder when going downstream than when going upstream, but nor did he paddle any less hard - i.e. his paddling was exactly the same when travelling in both directions.
[... and, yes, I know the answer (and both the easy and more complicated ways of getting it)- so I'll keep quiet for a while!]
Kind Regards, John
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