Brain teasers

[dustystreet]

0/4 !

just as well i turned down that offer to become the new egghead!

i did look on google maps afterwards and bowed my head in shame...

 

[Over The Hill]

Maine has got to be the furthest east although if PR was a state (which its not it'd give it a run for its money).

Excluded Puerto Rico

So what are your 4 guesses?

 

[marinyork]

Florida for south if it includes the keys. Alaska for west if it includes the Aleitian archipelago. Alaska for north I guess. Although I think east might actually have two answers depending on how you go.

 

[swee'pea99]

Spot on - You win the prize!

The original door has a 1 in 3 chance of being right and this is unaffected by the vacant door being opened (you already know one or other is vacant.

BUT by the vacant door being opened it makes the other door now a 1 in 2 chance. The chance is increased by the fact that only a vacant door will be revealed. That increase is not carried across to the original choice.

If you think of the process being repeated with 10 doors instead of 3 you see your chance increase each time a door is opened but only if you change doors.

I've heard this one before - it made no sense to me then; it makes no more now.

What's done is done. It cannot affect the situation now. The situation now is, there are two doors: one good, one bad. You can choose one, or you can choose t'other (ie, stick or change). It's 50/50. I really cannot see this any other way. Call me dumb.

 

[Haitch]

N = Alaska
E = Alaska
W= Alaska
S = Hawai

 

[marinyork]

Oh yeah Hawaii. I see you're thinking the same thing I am on definitions of east then Alan H.

 

[Haitch]

I didn't Google, 'twas on the radio this week.

 

[marinyork]

I didn't Google, 'twas on the radio this week.

Radio, what is that?

I think some Alaskan islands cross the international date line so you could regard them as furthest east. Depends on your definitions.

 

[Over The Hill]

N = Alaska
E = Alaska
W= Alaska
S = Hawai

Correct.

As soon as you go past 180 degrees west it becomes east.

 

[Over The Hill]

[quote name='swee'pea99']I've heard this one before - it made no sense to me then; it makes no more now.

What's done is done. It cannot affect the situation now. The situation now is, there are two doors: one good, one bad. You can choose one, or you can choose t'other (ie, stick or change). It's 50/50. I really cannot see this any other way. Call me dumb.[/QUOTE]


Look at it with 100 doors.
You choose one. The prize is behind only one door. So now if I open any of the remaining 98 doors nothing has changed (I will not open the one with the prize. So sticking with your same door you have a 1 in 100 chance.


Now do it again, this time you change.
Say I open 98 doors. The remaining door will have the benefit of the fact that I reveal only vacant doors thus increasing the chance that the remaining doors have the prize. The last remaining other door has the benefit of not being opened when the other 98 were opened.

But your origninal choice of door has not had its chance increased as it has not been an option to open as it was picked.

So now the original door is 1:100 the one remaining 1:2.

Simples

 

[Over The Hill]

Or think of it as a bag of 100 marbles with one white marble.
Take one out blind and hold it.
Now I take out 50 non white marbles.
Is it better to go for the one you are now holding (at 100to1) or dip in again at 50 to 1

 

[abchandler]

There are six outcomes depending on which door you choose and whether you change your mind and in total a 50/50 chance of winning. If you don't change you win 1 in 3. If you do, you win 2 in 3.

door chosen---change?----Result
right-----------no----------win
wrong 1--------no----------lose
wrong 2--------no----------lose
right-----------yes---------lose
wrong 1--------yes---------win
wrong 2--------yes---------win

 

[marinyork]

Correct.

As soon as you go past 180 degrees west it becomes east.

It's not as simple as that. Like I said, it depends on your definitions.

 

[Haitch]

It's not as simple as that. Like I said, it depends on your definitions.

In the same way that most of Europe (and bits of Britain) are not in the western hemisphere.

 

[swee'pea99]

I think about the marbles and it makes sense and then I think about the doors again and it doesn't and now my head hurts and I'm going to have to go away somewhere that has very dim lighting and drink a *lot* of beer, so thank you *very* much....don't call us we'll call you...

*sniff*