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ArcySparky
ARGH!

So simple...

The fact that it was a green threw me off... if it was a red or orange I'd have solved it like that!

as it was I was using all the knowledge gained from A-level statistics to try and solve it.

All well...

~Arcnowknowsnottooverthink...

Posted: Tue Aug 01, 2006 4:27 pm
Rand0m
I thought the answer was going to be
 Spoiler (Rollover to View): forever
because of the heavily stressed randoness - I guess the reason it isn't is because of the bit that says on average - ie
 Spoiler (Rollover to View): some people will see it first time, others will wait until Doomsday, but on average most people will be certain of having seen it by 140.
I think.

Posted: Tue Aug 01, 2006 10:39 am
Tufty
What I dont understand is that as it's completely random, i.e. as soon as it switches from one picture to the next it "forgets" which pictures have been shown, this fellow's portrait might never come up.

And also, if it was all 140 uniquely then on average then it would be 70, as out of 140 shots half the time he'd be in the first 70 and so on.

Hmmm.

Posted: Tue Aug 01, 2006 10:22 am
TopGun2
You're overcomplicating this card, it's only a green.

 Spoiler (Rollover to View): On average the portrait will appear once every 140 minutes

 Spoiler (Rollover to View): Personally I'd knock 1 minute off for the fact that one portrait is shown when he arrives but the answer doesn't do that

so the confirmed solve is:

 Spoiler (Rollover to View): 140

Posted: Mon Jul 31, 2006 3:11 pm
thereverendeg
It doesn't accept any of these:

 Spoiler (Rollover to View): 96 97 98

Posted: Mon Jul 31, 2006 2:22 pm
KingOfWrong
As fitzyfitz noted:
 Spoiler (Rollover to View): The probability of waiting k minutes, P(X=k) = p(1-p) k-1 where p is the chance of your picture appearing: 1/140

This distribution is:
 Spoiler (Rollover to View): X ~ Geometric(p)

Posted: Mon Jul 31, 2006 1:01 pm
fitzyfitz
 Spoiler (Rollover to View): probability of observer *not* seeing their portrait after X minutes is 139/140 ^ X (139/140)^96 = 0.502 (139/140)^97 = 0.499 so it takes 97 minutes to reach a >50% chance of seeing your own portrait

Posted: Sun Jul 30, 2006 5:07 pm
norman182
#128 Perplexing Portraits

card author sente

card text reads

Whilst attending the opening of the new "perplex city today" exhibit at the maitland museum, i noticed a large group of academy fellows gathered round a painting. moving closer, i saw that it was the latest work from the renowned artist hugo bonvini.
"Apparently hes painted 140 of us and the picture changes to a different one every minute its completely random though, johnstones come up twice in the last ten minutes!" explained one fellow.
"bonvini's a genius with a brush . i'm not leaving until i see my picture cant be too long now!" exclaimed another
Just then the picture changed once again to johnstone and i realised how long the fellow could expect to be waiting for his portrait to appear.
laughing to myself at how clever the artist was, i walked away, making a mental note to check none of the group belonged to the mathematics department.

How long should the fellow expect to wait on average?

Posted: Sun Jul 30, 2006 9:41 am
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