Monty Hall

[ebee]

It depends what you mean by sphere.

Most words (or phrases) have at least three possible slightly different meanings.

1/ Everyday ordinary use.

2/ A technical meaning depending upon your sphere (oops sorry!, field (oops), context in which it is discussed.

3/ A legal meaning.

Those three (or more) can differ so it`s better to give as much info as possible to what we really mean to convey.

 

[TonyW2]

What is the volume of a 10cm diameter sphere?
If there is a different answer to this puzzle when the sphere is 10cm and the drill of no diameter, but a constant answer when the size of drill and sphere are increased slightly (or a lot) what would be the answer if they were increased by a smaller amount than the minimum slight amount?

 

[TonyW2]

PS. I bet that some future googlers will be amazed to arrive at a DIY site

 

[EFLImpudence]

Is this a sphere?

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

A hollow what?

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".

If it is a sphere then the volume of the sphere.

 

[JohnW2]

What is the volume of a 10cm diameter sphere?

(500/3)π cu cm, which is about 523.6 cu cm

If there is a different answer to this puzzle when the sphere is 10cm and the drill of no diameter, but a constant answer when the size of drill and sphere are increased slightly (or a lot) what would be the answer if they were increased by a smaller amount than the minimum slight amount?

For any 'length of hole' (which is the only dimension specified in the question), there is only one answer, regardless of the diameter of the sphere - but, of course, there will be only one diameter of hole which will result in that particular 'length of hole' in a sphere of any given size. ... with the one proviso that the sphere obviously cannot be smaller in diameter than the length of the hole.

Kind Regards, John

 

[JohnW2]

Is this a sphere?

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

A hollow what?

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".

If it is a sphere then the volume of the sphere.

I think the problem is that you're trying to interpret as being a 'word puzzle' (like the Prime Minister one) something which has been established as a 'mathematical puzzle' for more than 80 years - and that, in turn, has caused to to try to propose a definition of 'the length of a hole' in an object which doesn't really make much sense (at least, to me).

Do I take it that your argument is that the volume of a sphere remains unchanged regardless of how much you chop out of it, and also that the only '10cm long hole' you can have drilled through a sphere (all the way through, going through centre) is one of zero diameter drilled through a sphere of 10cm diameter? (hence the answer you gave)

Kind Regards, John

 

[DetlefSchmitz]

John. I liked what you were doing with the attempt to make the solution intuitively clear. It doesn't do much for me yet, but it could be groundbreaking if you cracked it.

Unfortunately it would be the end of your internet anonymity.

 

[ban-all-sheds]

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"?

I think you've failed to grasp the essential point of the question...

However, what if, in 1985 it had been asked on Newsnight "What was the Prime Minister's name in 1950?"

Margaret.

 

[EFLImpudence]

Silly billy, Atlee wasn't called Margaret.

 

[ban-all-sheds]

that, in turn, has caused to to try to propose a definition of 'the length of a hole' in an object which doesn't really make much sense (at least, to me).

Cross-section through the remaining vaguely toroidal object:

 

[ban-all-sheds]

Silly billy, Atlee wasn't called Margaret.

He was at the weekends, but they kept it quiet.

 

[JohnW2]

John. I liked what you were doing with the attempt to make the solution intuitively clear. It doesn't do much for me yet, but it could be groundbreaking if you cracked it.

It wouldn't surprise me if someone has already got there. As I've said, I just find it very unlikely (and intellectually unsatisfying) to believe that the answer we see is purely the result of 'mathematical co-incidence' - i.e. just a chace quirk of the algebra.

Unfortunately it would be the end of your internet anonymnity.

I don't know about that. Mathematical (and undoubtedly other) sciences are littered with examples of people having published under pseudonyms (and sometimes become 'immortalised' under that pseudonyms) - how about "Student's t-test"?!

Kind Regards, John

 

[TonyW2]

What is the volume of a 10cm diameter sphere?

(500/3)π cu cm, which is about 523.6 cu cm

Only "about" ?

If there is a different answer to this puzzle when the sphere is 10cm and the drill of no diameter, but a constant answer when the size of drill and sphere are increased slightly (or a lot) what would be the answer if they were increased by a smaller amount than the minimum slight amount?

For any 'length of hole' (which is the only dimension specified in the question), there is only one answer, regardless of the diameter of the sphere - but, of course, there will be only one diameter of hole which will result in that particular 'length of hole' in a sphere of any given size. ... with the one proviso that the sphere obviously cannot be smaller in diameter than the length of the hole.

Kind Regards, John

And, as asked, when the increase from zero is less than required to reach the answer shown?

 

[JohnW2]

Cross-section through the remaining vaguely toroidal object:

Exactly. I tried to 'draw' one of those yesterday, but found that what software I have on my laptop wasn't very conducive!

Kind Regards, John

 

[EFLImpudence]

(500/3)π cu cm, which is about 523.6 cu cm

Is there a reason you wrote it like that?

I know the 500 is 4xr³ or d³/2 but that would not be apparent to anyone who didn't already know how to do it.