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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Green Puzzle Cards
#109 - Green - Infinite Series
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monkeytroll
Boot

Joined: 23 Oct 2005
Posts: 33

 		#109 - Green - Infinite Series
The architects of Perplex City's railroads loved building everything in straight lines - mountains, rivers, valleys - none of it mattered to them. There's still one stretch west of the city that continues for 100km with practically no turns.
Imagine there are two trains travelling towards each other at either end of the 100km stretch at 50km/h. Flying back and forth directly between the two trains at 75km/h is a bee that starts on the front of one of the trains when they're 100km apart, and immediately turns around to the other train as soon as it reaches it, and so on. How far will the bee have travelled in this zig zag fashion before the two trains meet?

Puzzle set by Kurt.

Map on back shows Wavelength, Jane Street, Horizon Drive.

Sorry no scan.
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PostPosted: Thu Nov 24, 2005 5:04 pm
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Kvasir
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Joined: 15 Oct 2005
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Spoiler (Rollover to View):
Fairly simple one really. The trains meet at the 50k mark, after travelling for precisely 1 hour. In one hour the bee travels 75k.


PostPosted: Thu Nov 24, 2005 5:48 pm
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Nightingale
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 		I don't mean this to sound cheeky but has that answer confirmed?

I thought that there was going to be a lot of working out involved as it seemed complicated - or is this a trick question?

Dazed and confused

Nightingale
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PostPosted: Fri Nov 25, 2005 1:17 pm
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European Chris
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 		I don't know if it's been confirmed but it's a lovely question
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PostPosted: Fri Nov 25, 2005 1:28 pm
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uneasyjd
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 		Yup.

Spoiler (Rollover to View):
It's 75.

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PostPosted: Sat Nov 26, 2005 1:19 pm
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Riiick
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Nightingale wrote:
I don't mean this to sound cheeky but has that answer confirmed?

I thought that there was going to be a lot of working out involved as it seemed complicated - or is this a trick question?

Dazed and confused

Nightingale

It is, that is certainly the sane and easy way to do it. However as the bee has to go back and forth an infinite number of times it is also be the sum of the following infinite series...

Spoiler (Rollover to View):
D = 60 + 60*0.2 + 60*0.2^2 + 60*0.2^3 + 60*0.2^4 + 60*0.2^5 + 60*0.2^6 + ...


Which can be solved with the following equation:
D = 60/(1-0.2)
=75


PostPosted: Sun Nov 27, 2005 7:49 am
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minnie the third
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Joined: 29 Dec 2005
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 		This is a basic maths question we did at school with other info added to confuse. the bee is flying for an hour at 75km/hour = 75. no convoluted formulas are needed at all.

PostPosted: Fri Jan 06, 2006 3:08 pm
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Riiick
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Joined: 29 Apr 2005
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Location: Canterbury, Kent, UK
minnie the third wrote:
This is a basic maths question we did at school with other info added to confuse. the bee is flying for an hour at 75km/hour = 75. no convoluted formulas are needed at all.

I know, I just wanted to illustrate the infinite series side of the card.

PostPosted: Sat Jan 07, 2006 7:55 am
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King Cody
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 		and for completness, These anwsers are Conferemed

Spoiler (Rollover to View):

1. French
2. Italian
3. German
4. Welsh
5. elvish
6. Danish
7. Japanese
8. Russian
9. Ghanaian
10. Kiswahili


PostPosted: Sun Dec 10, 2006 8:16 pm
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aliendial
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Joined: 29 Sep 2002
Posts: 3438
Location: Far Far Away. Nowhere Near You. Really.

 		OOps. Wrong thread, King Cody. I think that list is in the correct thread, (card #112) but thanks for the confirmation!
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PostPosted: Sun Dec 10, 2006 10:50 pm
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