Monty Hall

[EFLImpudence]

As I said, I think you're making it unnecessarily complicated.

Moi?

The puzzle

Exactly.

It was a puzzle, not a complex mathematical exercise to determine if you could work out the volume of two domes and a cylinder.

just relates to the object 'as it is' after the hole has been drilled.

It is still a sphere albeit with a part missing.

 

[EFLImpudence]

How deep is a hole in the ground which has a curved bottom?

That obvioulsy depends upon how one has defined depth.

To the bottom.

 

[JohnW2]

Exactly. It was a puzzle, not a complex mathematical exercise to determine if you could work out the volume of two domes and a cylinder.

... just relates to the object 'as it is' after the hole has been drilled.

It is still a sphere albeit with a part missing.

If you didn't know how it had been created, you could equally say the same of a toroid, cube, pyramid or anything other solid shape. Any of them could have started life as spheres and therefore be 'a sphere with a part(s) missing'.

Anyway, the real crux is this ... do you realise that the views/interpretations you are expressing today would render the problem unsolvable? Unlike the answer resulting from the correct interpretation, which is a single answer which remains true regardless of the diameter of the hole, if you want to include the removed 'domes at the end' as part of the 'length of the hole', then the answer would be different for every hole diameter - so one could not answer the puzzle without being told the hole diameter (and the answer you gave early on would only be true if the hole diameter were zero).

Kind Regards, John

 

[JohnW2]

How deep is a hole in the ground which has a curved bottom?

That obvioulsy depends upon how one has defined depth.

To the bottom.

So you've answered your own question. However, as I said, in the case of the object created in the puzzle, there is no such option - there is no physical 'bottom' of the hole, and the only 'length'/'depth' one can talk of is the length of the walls of the cylindrical hole. Adding on 'imaginery' bits, which no longer exist after the object has been created, really makes no sense!

How long is crankshaft in your car? - the length that it actually is, or the length of the casting from which it was machined?

Kind Regards, John

 

[EFLImpudence]

Precisely -

Or "What was the Prime Minister's name in 1971?"

However, this is another example of 'lack of clarity' in the question. It's actually totally ambiguous - so 'either' answer is, I suppose, correct.

That may be true but -

It depends on whether this is a serious question or another puzzle, not necessarily the lack of clarity.

If a puzzle being asked at a party where it may be one of several then the answer could be either David Cameron or Edward Heath.
The questioner can obviously claim the correct answer is the other depending on the reply so it is not possible to get it right.

On the other hand, if a serious question during Newsnight, because some one has forgotten then then the answer is Edward Heath because no one is going to think David Cameron has changed his name.


Vic and Bob - "Name a junction on the M1"
Contestant - "Junction Seven?"
Vic and Bob - "Nope, wrong, it's junction twelve"

 

[JohnW2]

Or "What was the Prime Minister's name in 1971?"

However, this is another example of 'lack of clarity' in the question. It's actually totally ambiguous - so 'either' answer is, I suppose, correct.

That may be true but - It depends on whether this is a serious question or another puzzle, not necessarily the lack of clarity.

That's one way of looking at it. I would say that it involved a deliberate lack of clarity (to deliberately produce an ambiguity) in order to make it a 'puzzle', rather than a 'serious question'.

If a puzzle being asked at a party where it may be one of several then the answer could be either David Cameron or Edward Heath.The questioner can obviously claim the correct answer is the other depending on the reply so it is not possible to get it right.

It could happen like that, but it's then hardly even a 'puzzle'. I think it more likely that, given that most people would probably answer Edward Heath, the questioner would be 'looking for' an answer of David Cameron, and would (maybe grudgingly) admit that was the 'correct' answer if given.

The sphere puzzle is different. If the question were stated very clearly and unabiguously (and there's no reason why it shouldn't be) then there is just one correct answer (and even that requires at least some mathematical knowledge).

Kind Regards, John

 

[ban-all-sheds]

Precisely -

Or "What was the Prime Minister's name in 1971?"

However, this is another example of 'lack of clarity' in the question. It's actually totally ambiguous - so 'either' answer is, I suppose, correct.

That may be true but -

It depends on whether this is a serious question or another puzzle, not necessarily the lack of clarity.

But is it lack of clarity?

Or is it a precise "What was the Prime Minister's name in 1971?", not "What was the name of the Prime Minister in 1971?"?

 

[JohnW2]

But is it lack of clarity? Or is it a precise "What was the Prime Minister's name in 1971?", not "What was the name of the Prime Minister in 1971?"?

I really don't see the difference between those two wordings - I would say that both are equally ambiguous. To be unambiguous, you would have to use words like "What was the present Prime Minister's name in 1971?" (or, even better, "What was the name in 1971 of the person who is the present-day Prime Minister?") and "What was the name of the person who was Prime Minister in 1971"?

EFLI suggested that, if it had been a 'serious question' on Newsnight, that there would have been no ambiguity, because "no-one is going to think that the Prime Minister has changed his name". However, what if, in 1985 it had been asked on Newsnight "What was the Prime Minister's name in 1950?" ? - that would have been a definite ambiguity

Kind Regards, John

 

[EFLImpudence]

That's one way of looking at it. I would say that it involved a deliberate lack of clarity (to deliberately produce an ambiguity) in order to make it a 'puzzle', rather than a 'serious question'.

Precisely. In this thread it was a puzzle.

If the answer is intended to be David Cameron then it is always going to be a puzzle - 'rarely' the case with Jeremy Paxman.

The sphere puzzle is different. If the question were stated very clearly and unabiguously (and there's no reason why it shouldn't be) then there is just one correct answer (and even that requires at least some mathematical knowledge).

But unless Bas contradicts ??? then it was a puzzle because of the lack of detail.

 

[EFLImpudence]

But is it lack of clarity?

Yes, because it is a puzzle.

Or is it a precise "What was the Prime Minister's name in 1971?", not "What was the name of the Prime Minister in 1971?"?

No, anyone seriously requiring the name of the prime minister at some time in the past would say "Who was the Prime Minister in 1971".

 

[EFLImpudence]

However, what if, in 1985 it had been asked on Newsnight "What was the Prime Minister's name in 1950?" ? - that would have been a definite ambiguity

That would be ambiguous but it is the only time it would be applicable but then she always did cause a lot of trouble.

 

[JohnW2]

The sphere puzzle is different. If the question were stated very clearly and unabiguously (and there's no reason why it shouldn't be) then there is just one correct answer (and even that requires at least some mathematical knowledge).

But unless Bas contradicts ??? then it was a puzzle because of the lack of detail.

I stand open to correction, but I don't think that BAS did intend it to be a puzzle by virtue of a lack of detail/clarity. I believe that he intended it as the 'mathematical puzzle' which it always has been (since 1932, if not before). As I said, that 'mathematical puzzle' is not in any way undermined by posing it with precise, clear and complete wording, maybe something like:

• "A drill is used to make a hole all the way through a sphere, going through the centre of the sphere. The length of a side of the resulting cylindrical hole resulting in the object created is 10cm. What is the total volume of material remaining in the object after the hole has been drilled"

Anyway, as I said, if your interpretation was different than that (and, instead, what you have been suggesting today), it is not possible to give an answer, and the one which you gave would only be correct in the one hypothetical scenario of the hole having a zero diameter!

Kind Regards, John

 

[EFLImpudence]

Is this a sphere?

If so, what is its volume, assuming the diameter is 10cm?

Not a trick question.

 

[ebee]

EFLImpudence,

you are a naughty naughty boy

 

[JohnW2]

Is this a sphere?

Not really - it's a hollow sphere with multiple holes in it!

If so, what is its volume, assuming the diameter is 10cm? Not a trick question.

Maybe not a trick question, but one seriously lacking in clarity - i.e. multiple ambiguities. You would have to specify what you meant by "its volume" - the volume of the material of which it's made, the volume the material would have had if the holes hadn't been there, the volume which would have been contained by the material if the holes hadn't been there, the volume that the outer surface of the material would have contained had the holes not been there ... etc. In the absence of detail, I agree that most people would probably calculate the last of those (resulting in your famous answer of ~523.6 cu cm, assuming that 10cm was the outside diameter), but that's far from the only interpretation of the question!

Kind Regards, John