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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Yellow Puzzle Cards
[PUZZLE] #088 - Yellow - Pyramidal
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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dopefiend
Decorated


Joined: 11 Apr 2005
Posts: 182
Location: London, UK

[PUZZLE] #088 - Yellow - Pyramidal

worth 22 perplex points
signature: sente
text:

We've all encountered pyramid schemes which promise you an easy path to millions if you send a little cash to a few people on a list and forward the message to all of your grateful friends. Few realise that pyramid schemes, if unchecked, have the potential to ruin entire countires.

During 1996-1997, a number of companies operated pyramid schemes in Albania that collectively attracted nearly 2 million people out of a population of 3.5 million. Three of the companies alone had deposits worth $390 million, or 15% of GDP. Eventually the government banned the schemes but couldn't prevent the country's descent into chaos.

Imagine the extremely unlikely situation of a pyramid scheme sweeping Perplex City, where each participant recruits six people and sends money to people in the levels above them. If the population of Perplex City is 10 million, how many levels will it take for the pyramid scheme to run out of new members to recruit, leaving lots of people very broke and unhappy?
pyramidal.JPG
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pyramidal.JPG

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PostPosted: Tue Jul 12, 2005 1:39 pm
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firefox
Unfettered

Joined: 28 Jul 2004
Posts: 333

id say:
Spoiler (Rollover to View):

level 10


umm, i dont know if they are counting the first person as a level or what but here is some reasoning:

Spoiler (Rollover to View):


first off theres 1 person. (Total: 6^0)
he recruits 6 people. (Total: 6^0+ 6^1)
each of those 6 people recruit 6 people of their own, 6x6 or 6^2
(Total: 6^0+6^1+6^2)

the pattern is + 6^x+1 ( i think)

so you do this until your Total first hits over 10,000,000

which is at 6^0+6^1+6^2+6^3+6^4+6^5+6^7+6^8+6^9 = 12,046,579

or Level... 10 i guess. If you are counting 6^0 or the initial person as level 1.



umm i could be wrong Rolling Eyes maths is not my strong point.

PostPosted: Tue Jul 12, 2005 2:02 pm
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dusty2229
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Joined: 14 May 2005
Posts: 128
Location: London

Added to card catalog
#088 Pyramidal (back).jpg
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#088 Pyramidal (back).jpg


PostPosted: Sun Jul 17, 2005 3:22 am
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Riiick
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Joined: 29 Apr 2005
Posts: 82
Location: Canterbury, Kent, UK

If you look at the image on the card it suggests the first level is 6 people.

This means the pyramid scheme runs out of people at the 9th level

PostPosted: Thu Aug 04, 2005 5:33 pm
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C_Brennan
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Joined: 02 Sep 2004
Posts: 236
Location: Pittsburgh, PA

Rick is right, the pyramid scheme ends at approximately the 9th level.

The card is an equation using the base log, where we know the answer (10,000,000) and we know that we need some power of X to equal about 10,000,000. The equation is:

6^x = 10,000,000

Which we can reduce down to:

x = log(6) * 10,000,000

Which in log base 10 is:

x = log (10,000,000) / log (6)

Which equals approximately 8.99, rounding up to reach 9. This means that the pyramid scheme will end at the 9th level. (6 to the 9th power is approximately 10,000,000)
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PostPosted: Fri Aug 05, 2005 1:57 pm
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Bahamoth
Boot

Joined: 07 Aug 2005
Posts: 24
Location: Reading

Perhaps I'm simple. but I just did 6x6x6x6x6x6x6x6x6
Is this the same just expressed inelequently?

PostPosted: Sun Aug 07, 2005 5:27 pm
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Shockt
Boot


Joined: 19 Feb 2005
Posts: 36

You guys forget that you must add the result from each level to the total..

Spoiler (Rollover to View):
1 - 6 people start = 6 total people
2 - 36 new people = 36+6 = 43 total people
3 - 216 new people = 216+36+6 = 259 total people
4 - 1296 new = 1555 total
5 - 7776 = 9331
6 - 46656 = 55987
7 - 279936 = 335923
8 - 1679616 = 2015539
9 - 10077696 = 12093235

Still ends at the 9th step but 12,093,235 total people were recruited by the end of the 9th meaning the cycle would be completed before then. I really dont know what these solutions mean if anything...

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PostPosted: Mon Aug 08, 2005 6:03 am
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Bahamoth
Boot

Joined: 07 Aug 2005
Posts: 24
Location: Reading

I just figured the numbers before wouldn't add up to anything too significant.

PostPosted: Mon Aug 08, 2005 6:27 am
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fuegomanchego
Boot

Joined: 08 Apr 2005
Posts: 10
Location: Sydney, Australia

Level 10. I go with Firefox. There is 1 person at the top, not 6. Its a pyramid scheme, not a trapezium scheme.

PostPosted: Tue Aug 09, 2005 12:07 am
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Bahamoth
Boot

Joined: 07 Aug 2005
Posts: 24
Location: Reading

You may say that, but the card says differently. The card says 6 at the top. I think I'm gonna have to go with the card on this one, although you say 10 with such authority Wink
It's 9 levels.

Aaaaaaand relax.

PostPosted: Tue Aug 09, 2005 5:40 am
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swampy353
Kilroy

Joined: 09 Aug 2005
Posts: 1
Location: Dublin, Ireland

Real answer??

I think that there are nine levels. 6^9 = 10,077,696 which is closer to the 10 million figure then was given before.

PostPosted: Tue Aug 09, 2005 4:00 pm
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fuegomanchego
Boot

Joined: 08 Apr 2005
Posts: 10
Location: Sydney, Australia

Quote:
You may say that, but the card says differently. The card says 6 at the top. I think I'm gonna have to go with the card on this one, although you say 10 with such authority
It's 9 levels.


So it does. Squiniting at the scan it does say on the pyramid that level 1 is 6 people - i was only going off the text. So, fair enough. Tail between legs, i'll have to agree with 9.

PostPosted: Tue Aug 09, 2005 11:52 pm
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tangohead
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Joined: 27 Apr 2005
Posts: 73
Location: North West England (Wigan)

Spoiler (Rollover to View):
confirmed it is the 9th step - i got my points Very Happy

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PostPosted: Wed Oct 12, 2005 6:27 am
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illuminati_dk
Boot


Joined: 16 Oct 2003
Posts: 43
Location: Denmark

Mark This one [SOLVED] just confirmed the answer and got my points

Spoiler (Rollover to View):
9

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PostPosted: Tue Oct 25, 2005 6:47 am
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