Monty Hall

[ebee]

Monty Hall.

Following on from that thread containing a mammoth discussion about RCDs and Monty Hall etc etc
(apologies to the OP for taking his thread off at a tandem)

I looked it up in Wikipedia and came across the one with three boxes
A/ 2 Gold coins
B/ 2 Silver
C/ one of each.

I fell into the same trap again even though, on reflection, I did see the explanation a few years back.

Daft I know, but instincts often apply in hasty decisions rather than logical thought .

LOL.

That should teach me

 

[viewer]

Once you know the answer (2/3 on one side 1/3 on your side) it becomes clear, but it isn't intuitive. Like many things the mathematical or scientific explanation and even observations go against the way the human brain seems to be programmed; the Bernoulli effect is a good example. Why should this matter in a DIY electrical forum? Because the "common sense" argument doesn't work in real life and "common sense" meaning intuitive logic is not the same as "common knowledge" although it is often assumed to be the same. This is one reason why calling posters 'idiots' is unhelpful; our intuitive conclusions are so deeply seated in the way our brain works that it can be difficult to even consider a different result to the problem.

 

[ban-all-sheds]

If I drill a 10cm long hole right through a solid sphere, along an axis, what is the volume of the original sphere remaining?

 

[JohnW2]

If I drill a 10cm long hole right through a solid sphere, along an axis, what is the volume of the original sphere remaining?

I think you need to express that a bit (maybe a lot ) more clearly (and perhaps provide a bit more information) - at least, you do for me!

Kind Regards, John

 

[EFLImpudence]

523.6 cu.cm.

 

[JohnW2]

523.6 cu.cm.

I thought that 523.6 was about the "Number of loaded conductors"?

Kind Regards, John

 

[bernardgreen]

If I drill a 10cm long hole right through a solid sphere, along an axis, what is the volume of the original sphere remaining?

The same as before, only some of it is now a pile of swarf on the floor.

But not true if your drill bit runs hot and some of the sphere is burnt, vapourised or otherwise destroyed.

 

[ebee]

Well 523.6 ish would be the original volume of the sphere in cu cm, in a sphere of 10 cm diameter.
I get that bit of it.

So a drill 10cm long of zero diameter (which is impossible) would satisfy that.
I think any diameter of drill up to 10 cm dia would still need a total movement of 10 cu to drill thru.

Diameter of drill not stated.
OK I`m flummoxed !

 

[ban-all-sheds]

I think you need to express that a bit (maybe a lot ) more clearly (and perhaps provide a bit more information) - at least, you do for me!

I take a sphere, and I drill a hole right through the middle. That hole is 10cm long.

Ignoring bernard's nonsense about swarf and smoke, what's the volume remaining?

 

[DetlefSchmitz]

If the question had been in, say, a puzzle book, then we wouldn't have any difficulty answering it. And Ebee got very close. The problem is that people may be suspecting Bas's motives, or that he left something out.

If you assume that he gave enough information, and that there is a single simple answer, then it is the number which was mentioned above several times, because a simple example reduces the problem to an easy calculation.

Proving the general applicability is a little harder, but wasn't asked for.

By the way, is it only me that started (mistakenly) thinking that the REM song 'Monty Got a Raw Deal' was based on Monty Hall?

Edit: And of course EFLImpudence got it first.

 

[riveralt]

So following on from that if volume is a three dimensional occupied space removing any part of it would not affect that the total volume.
So the 'number of loaded conductors' via JohnW2 is correct.

 

[securespark]

The important bit to clock is this: Whatever the diameter of the sphere, and hole, the answer will be the same.

The two numbers (sphere and hole sizes) are not independent of each other and the volume that remains when the material is removed is constant.

The volume remaining equals the complete sphere.

 

[ebee]

Mmmm well he did ask the volume of the sphere rather than the volume of the solid still remaining therefore the volume of the sphere is still the same.

In the same way that a glass full of water and a glass half full of water and a glass with no water in would usually all be completely full - either of water, air or a mixture of both.

 

[seasickstevie]

The two numbers (sphere and hole sizes) are not independent of each other . . .

?
But it could be a big sphere and a thin drill. Or a relatively small sphere and relatively fat drill.



I'm obviously missin' summat !

 

[ebee]

Reminds me a bit of the old one (pre-decimal).

How many pennies in a dozen? - A 12 (a Shilling - 5p these days).

Then, next question, how many halfpennies in a dozen? (most of us initially answered 24!).

Methinks that these days with our automatic links with a dozen pennies being a shilling removed that it would be less common, even by those brought up on £ s d, to get that one wrong as often.