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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Green Puzzle Cards
#128 Perplexing Portraits
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norman182
Boot


Joined: 16 Apr 2006
Posts: 14

 		#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?

PostPosted: Sun Jul 30, 2006 11:41 am
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fitzyfitz
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Joined: 03 Jan 2006
Posts: 31
Location: Nottingham, UK
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

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PostPosted: Sun Jul 30, 2006 7:07 pm
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KingOfWrong
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Joined: 05 May 2006
Posts: 45

 		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)


PostPosted: Mon Jul 31, 2006 3:01 pm
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thereverendeg
Veteran

Joined: 16 Jul 2006
Posts: 74
Location: Rochester, NY

 		It doesn't accept any of these:

Spoiler (Rollover to View):
96
97
98

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PostPosted: Mon Jul 31, 2006 4:22 pm
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TopGun2
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Joined: 30 Nov 2005
Posts: 30
Location: Cambs, UK

 		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

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PostPosted: Mon Jul 31, 2006 5:11 pm
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Tufty
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Joined: 12 Aug 2005
Posts: 27
Location: UK

 		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.

PostPosted: Tue Aug 01, 2006 12:22 pm
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Rand0m
Decorated


Joined: 14 Mar 2006
Posts: 271
Location: London

 		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.
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PostPosted: Tue Aug 01, 2006 12:39 pm
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ArcySparky
Boot


Joined: 04 May 2006
Posts: 51
Location: Belfast, Northern Ireland

 		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...

PostPosted: Tue Aug 01, 2006 6:27 pm
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The V.G.P.S.
Boot

Joined: 01 Aug 2006
Posts: 16

 		Answer is def. as above. Remember its not asking for any guarantee,its the average that counts Wink

PostPosted: Wed Aug 02, 2006 8:19 am
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Guin
Unfettered


Joined: 11 Jan 2006
Posts: 400
Location: Antartica

 		it would have been funnier if it had been

Spoiler (Rollover to View):
a mirror

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PostPosted: Wed Aug 02, 2006 3:15 pm
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Rifflesby
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Joined: 15 Apr 2006
Posts: 23
Location: Mesa, AZ

 		I object to the wording of this card. The answer is only [what it is] if you're looking for the average of all the lengths of time it took everyone to see their own portraits.

But the question *as given* is asking how long this particular guy should expect to wait, "on average", and for that question fitzyfitz's math is correct.

Unless, y'know, I'm just totally reading it wrong. Always a possibility :)

PostPosted: Sat Aug 05, 2006 3:53 am
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European Chris
Unfictologist


Joined: 19 Jul 2005
Posts: 1264
Location: London's trendy Whitechapel
Rifflesby wrote:
I object to the wording of this card. The answer is only [what it is] if you're looking for the average of all the lengths of time it took everyone to see their own portraits.

But the question *as given* is asking how long this particular guy should expect to wait, "on average", and for that question fitzyfitz's math is correct.


The maths is right, but doesn't answer the right question. It's not asking how long someone should wait to have a 50% chance of seeing themselves but how long on average time someone should wait-and the answer to that is related to the expected value

It's simlar to 'infinty series' (with the train and the bee), it just gives you more information than you need to try and confuse you. So I'm sure you do object to the wording of the card, but that's the bit that makes the puzzle.
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PostPosted: Sat Aug 05, 2006 11:34 am
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mikew03
Greenhorn

Joined: 24 May 2006
Posts: 3
Spoiler (Rollover to View):

I strongly disagree that the answer is 140. Assuming it really is a random distribution on average a person will wait half that time to see his picture. I don't see anything tricky about the wording. The answer is simply wrong.

If I walk into a room where 140 pictures are being randomly displayed (one of which is a picture of me) on average I will wait 70 minutes to see mine. It might be one minute, it might be 140. But the average IS 70.

Just ask the people working on the 13th labor, they are at 60% now and are getting nervous they don't have the right code to solve the problem, because on average they should have solved it by now.


PostPosted: Thu Aug 10, 2006 2:47 am
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Agent Lex
Entrenched


Joined: 11 May 2006
Posts: 1188
Location: No longer London, still in England
mikew03 wrote:
Spoiler (Rollover to View):
If I walk into a room where 140 pictures are being randomly displayed (one of which is a picture of me) on average I will wait 70 minutes to see mine. It might be one minute, it might be 140. But the average IS 70.

Spoiler (Rollover to View):
It might be 1 minute, it might be 280, it might be 5 weeks until you see it. The average is (close enough to) 140.


Quote:
Spoiler (Rollover to View):
Just ask the people working on the 13th labor, they are at 60% now and are getting nervous they don't have the right code to solve the problem, because on average they should have solved it by now.

Spoiler (Rollover to View):
That's a different problem, because with each code processed it's done and will never need to be processed again, while this picture can obviously show the same person 3 times in 10 minutes or so, as seen on the card with Johnstone.


PostPosted: Thu Aug 10, 2006 6:50 am
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situp
Greenhorn

Joined: 04 Aug 2006
Posts: 4

 		There's 140 pictures, and I am 1 of those 140 pictures, so on average I will appear 1/140 times. There's no complication here. It really is as simple as it seems.

PostPosted: Fri Aug 11, 2006 10:41 pm
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