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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Purple Puzzle Cards
[flame set] #167 - Circular
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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Fuseunderground
Decorated

Joined: 17 Dec 2005
Posts: 151

 		It is usually good practice to use as many decimal as you can,
this stops errors down the line due to rounding.

In this case the fact that it tells you to have the answer to 4 d.p.
implies you should use Pi to at least 5/6 d.p. because you will have to round it to get the answer.

[as with any answer using Pi, you could list any number of decimal places]
so you use more than the amount you need to give the answer in to avoid the errors you illustrated above.

Rich

p.s. the calculator I had to hand was just a cheap desk one,
most can give 9 d.p. even mobile phones, so it's not unreasonable to assume you could give an answer to the accuracy of 4d.p.'s
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Like your hero TJ Hooker you tackle challenges head-on with determination and vigour paying scant attention to the law. This devil-may-care attitude may work for fictional crimefighters but it can be counterproductive in real life.

PostPosted: Thu Apr 27, 2006 1:36 pm
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Fuseunderground
Decorated

Joined: 17 Dec 2005
Posts: 151

 		Windows Calculator has Pi as:

3.1415926535897932384626433832795

which I think is accurate enough Wink
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Like your hero TJ Hooker you tackle challenges head-on with determination and vigour paying scant attention to the law. This devil-may-care attitude may work for fictional crimefighters but it can be counterproductive in real life.

PostPosted: Thu Apr 27, 2006 1:37 pm
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Hunting4Treasure
Unfettered


Joined: 06 Aug 2005
Posts: 385
Location: Tampa Bay Area, FL USA

 		I learn something new everyday... Thanks! Wink

My original problem (and maybe Sarah's?) was not extending the decimal places for Pi far enough. I still got the right answer, just not the *first* time. Razz

I've been out of school a loooong time. It's true: "If you don't use it, you'll lose it!" I'll keep your advice in mind, for next time! Wink
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PostPosted: Thu Apr 27, 2006 1:58 pm
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Hobbess
Kl00


Joined: 19 Dec 2005
Posts: 42
Location: Glasgow

 		My question is how did people calculate the area of the circles?

Given that all it is asking for is the radius I measured the diameter from some cut outs and then got stuck trying to spot a pattern and to get anything more accurate than 1 decimal place.

PostPosted: Wed May 03, 2006 6:03 pm
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baf
Boot

Joined: 29 Mar 2006
Posts: 46

 		For my part, I measured the diameter as closely as I could (which was to one very wobbly decimal place, which is about the width of the line around the circle), then figured the areas based on those diameters. The result was never a whole number, but it was always close enought that I could easily assume that the area was supposed to be a whole number and ascribe the difference to the inaccuracy of my measurement.

I suspect most solvers did the same.

PostPosted: Wed May 03, 2006 6:30 pm
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GasparLewis
Unfettered


Joined: 19 Nov 2005
Posts: 474
Location: vicinty of NYC

 		Personally, I just think it's a tad odd that the answer involves
Spoiler (Rollover to View):
the Fibonacci series

when another card,
Spoiler (Rollover to View):
Sweet Dreams, a yellow,

already has been based on it.

*shrugs shoulders* Cool

PostPosted: Thu May 04, 2006 11:01 am
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Fuseunderground
Decorated

Joined: 17 Dec 2005
Posts: 151
GasparLewis wrote:
Personally, I just think it's a tad odd that the answer involves 'spoiler'


Well there are only so many
Spoiler (Rollover to View):
famous mathmatical series

and the yellow card was a more obvious usage of it,
where as this is a purple the relationship was more obtuse.

I think people here generally find answers more easily than the 'average player'
Because of the huge amounts of experience and skills some people have.
not me though, obviously Worshippy
_________________
Like your hero TJ Hooker you tackle challenges head-on with determination and vigour paying scant attention to the law. This devil-may-care attitude may work for fictional crimefighters but it can be counterproductive in real life.

PostPosted: Thu May 04, 2006 11:21 am
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BethThomlinson
Boot

Joined: 21 May 2006
Posts: 17
Location: California, USA

 		How many decimal places to use?
I used
Spoiler (Rollover to View):
pi to 5 decimal places,
since the answer was supposed to be to 4 places. If you start with
Spoiler (Rollover to View):
3.14159
all the calculations will work out.

PostPosted: Wed May 31, 2006 3:05 pm
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Cinana
Boot

Joined: 02 Jun 2006
Posts: 62
Location: Washington State, USA
sarahbarnsley wrote:
For those of you like me who dont really have a clue about maths, this is how i finally solved this card after a lot of trial and error.

Spoiler (Rollover to View):
The area of the circles rounded up/down comes to 1 2 3 5 8 13. This follows the fibonacci series - the next one in the series is 21. I simply divided 21 by 3.1415 (pi to 4 dec places) and then worked out the square root of that answer. This gave me the radius.


I did take about 10 attempts to solve this though so i was impressed when i finally managed it.


Thanks very much for the solve! Smile

PostPosted: Tue Jun 13, 2006 12:36 pm
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gemgenie
Greenhorn

Joined: 29 Apr 2006
Posts: 7
Location: Sheffield, UK
GasparLewis wrote:
Personally, I just think it's a tad odd that the answer involves
Spoiler (Rollover to View):
the Fibonacci series

when another card,
Spoiler (Rollover to View):
Sweet Dreams, a yellow,

already has been based on it.

*shrugs shoulders* Cool


Gaspar look at the way the circles are placed on the card - Nice clue!

PostPosted: Sun Jul 16, 2006 2:18 pm
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mama_needs_a_new_car
Boot

Joined: 16 Jun 2006
Posts: 33

 		Thanks to all of thee who are smarter than me!

I must confess to finall throwing in the towel, and bipping over here to visit my clever friends and steal the answer.

Thanks for being here!!!

PostPosted: Sat Jul 29, 2006 12:44 am
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X9Tim
Boot

Joined: 29 Sep 2006
Posts: 16
Fuseunderground wrote:
It is usually good practice to use as many decimal as you can,
this stops errors down the line due to rounding.

In this case the fact that it tells you to have the answer to 4 d.p.
implies you should use Pi to at least 5/6 d.p. because you will have to round it to get the answer.

[as with any answer using Pi, you could list any number of decimal places]
so you use more than the amount you need to give the answer in to avoid the errors you illustrated above.


Although its a long time since I was at school, I recall a set of rules about estimating from chemistry & physics as well as maths:

    When you square a number, you get exactly twice as many decimals, so when you take a square root, you only can only estimate to half the decimal places.


This implies that to get 4 decimals you need to use 8 in the value of pi. Clearly, by your experience, you get a good estimate with only 5 decimals, but with 8 (or 9 to avoid rounding errors) you KNOW you will get it close enough.

PS. I used Excel which seems to give pi to about 14 decimals

PostPosted: Sat Oct 07, 2006 7:16 am
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banditvj@Lilly
Guest


 		Circles
Diameter
Quick question if I may be so bold as to ask, but where are the circles to be measured from? Is it the outer rim (the outside the black lines) or the inner (where the blue circle meets the black rim)?

Hayelp! Even managed to blag a set of Vernier calipers to help me solve it!

Banditvj

PostPosted: Mon Nov 13, 2006 9:12 am
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Scribe
Unfettered


Joined: 09 Jun 2006
Posts: 300
Location: Brighton, UK

 		banditvj: measuring the outer diameter (i.e. including the black border) will make the puzzle easier to 'spot', IMHO Smile
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PostPosted: Fri Dec 22, 2006 9:44 am
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smartyman
Boot

Joined: 14 Feb 2007
Posts: 22
gemgenie wrote:
Gaspar look at the way the circles are placed on the card - Nice clue!

Sorry, I know I'm 9 months late to the party, but I'm a slow starter, so what the heck...

The arrangement of the circles, plus the background was what tipped me off to what the pattern might be.
Spoiler (Rollover to View):
Discussions of the Fibonacci Sequence almost always make reference to the Fibonacci Spiral, and the circles were arranged in a way that made me think they might spiral as the series continued. Also the beach scene made me think of shells, and the Nautilus shell is often cited as an example of a Fibonacci Spiral that can be found in nature.

Now, I just wonder if that's the author himself featured in the picture!

PostPosted: Tue May 22, 2007 8:31 pm
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