Author
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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?
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Posted: Tue Jul 12, 2005 11:39 am
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 maths is not my strong point.
Posted: Tue Jul 12, 2005 12:02 pm
dusty2229
Veteran
Joined: 14 May 2005 Posts: 128 Location: London
Added to card catalog
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Posted: Sun Jul 17, 2005 1:22 am
Riiick
Veteran
Joined: 29 Apr 2005 Posts: 79 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
Posted: Thu Aug 04, 2005 3:33 pm
C_Brennan
Decorated
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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Posted: Fri Aug 05, 2005 11:57 am
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?
Posted: Sun Aug 07, 2005 3:27 pm
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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16/100=7
Posted: Mon Aug 08, 2005 4:03 am
Bahamoth
Boot
Joined: 07 Aug 2005 Posts: 24 Location: Reading
I just figured the numbers before wouldn't add up to anything too significant.
Posted: Mon Aug 08, 2005 4:27 am
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.
Posted: Mon Aug 08, 2005 10:07 pm
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
It's 9 levels.
Aaaaaaand relax.
Posted: Tue Aug 09, 2005 3:40 am
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.
Posted: Tue Aug 09, 2005 2:00 pm
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.
Posted: Tue Aug 09, 2005 9:52 pm
tangohead
Veteran
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
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Posted: Wed Oct 12, 2005 4:27 am
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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Posted: Tue Oct 25, 2005 4:47 am
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