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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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SilentlyBroken
Boot

Joined: 02 Mar 2006
Posts: 37

 		[flame set] #167 - Circular
Signed by Caine. This card has a playing card symbol of 4 spades, and lettery bits.

The text reads:

Quote:
Each circle in this sequence increases in size. What is the radius of the next circle in this sequence, in centimetres, to four decimal places?


[edited to add diameters of circles]

From smallest to largest: 1.2cm, 1.65cm, 2cm, 2.6cm, 3.25cm, 4.1cm

Please allow margin for error Smile

The map back reads:

Quote:
Azad Park

Situated in the centre of a business and residential district, Azad Park contains a small wood and lake. Football pitches at the north end are used by the nearby Borfield School during the day but are open to the public on selected evenings. The park is also popular among runners not quite ready for the trails of Polygon Park.


[edited to change the mapback, uploaded the wrong one]
card167res.jpg
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card167res.jpg
card167mapbackres.jpg
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card167mapbackres.jpg

PostPosted: Thu Apr 06, 2006 2:57 pm
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Grizy
Veteran

Joined: 19 Nov 2005
Posts: 89
Location: Preston, UK

 		If you need some help on this

Spoiler (Rollover to View):
The area of the circles follow a famous number series


PostPosted: Thu Apr 06, 2006 7:46 pm
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doublecross
Unfettered


Joined: 25 Jul 2005
Posts: 588
Location: London, UK

 		Note that the guest puzzle architect is our very own Brian Enigma!
_________________
xx

PostPosted: Thu Apr 06, 2006 7:49 pm
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badbarry
Veteran

Joined: 10 Mar 2006
Posts: 140
Location: London

 		I see that many people (clearly cleverer than i) have now solved this one. As a non mathematician i did get the tape measure out and try the pi r squared stuff but nothing seemed to spring to mind. Any more obvioius hints for the non-gifted?

PostPosted: Sat Apr 08, 2006 6:46 pm
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hello
Guest


 		Could it be the fibonacchi (spelling?) sequence?
phi?

fibonacchi sequence=
t+(t-1)=t+1 if t=term of the sequence
0, 0, 1, 1, 2, 3, 5, 8, 13...

phi=1.6something
it's reciprocal is itself -1
only just learning about it...

PostPosted: Sun Apr 09, 2006 12:30 am
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tizer
Guest


 		hi is there any further hints to help solve this card as im finding it quite difficult

PostPosted: Sun Apr 09, 2006 7:19 pm
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sarahbarnsley
Guest


 		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.

PostPosted: Mon Apr 10, 2006 4:28 pm
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Hunting4Treasure
Unfettered


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

 		Another hint:
Spoiler (Rollover to View):
The final answer you get will have the 5th decimal place number as '7', but totally *ignore* it, and do *not* round up the 4th decimal place number! Confused

_________________
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Energy (Power) = Mind Candy's Cube
PerplexCityTrades - Hunting4Treasure

PostPosted: Fri Apr 21, 2006 12:30 am
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whtknight124
Kilroy

Joined: 24 Apr 2006
Posts: 1
Location: USA

 		more hints
ok can anyone be a little more specific. still am not doing something right.

PostPosted: Tue Apr 25, 2006 10:11 am
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ALISDAIRPARK
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Joined: 27 Nov 2005
Posts: 1646
Location: Everywhere else

 		For the hints, if you use the correct figure for Pi, then ignore hunting for treasure as that number won't be there, and you can correctly round to 4 decimals.
_________________
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PostPosted: Wed Apr 26, 2006 7:03 pm
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Hunting4Treasure
Unfettered


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

 		Sarah clinched it for me. Wink

And, if you follow her formula, that number I spoke about above, *will* be there. My first entered answer was wrong (rounding it up because '7' was the 5th number). I was just trying to help others avoid a wasted wrong entry. Confused
Spoiler (Rollover to View):
If you divide 21 by only 3.14, you get:
6.6878980891719745222929936305732
Square root is:
2.5860970765174254228237765816933
So that does't work (2.5860 or 2.5861 is *not* the answer)

Divide 21 by 3.141, you get:
6.685768863419293218720152817574
Square root is:
2.5856853759534034265114669498199
That doesn't work either 2.5856 or 2.5857 is *not* the answer)

Divide 21 by 3.1415 (as Sarah suggested), you get:
6.6847047588731497692185261817603
Square root is:
2.5854795993921804234790871187222
This *is* the answer! But, see the '7' in the 5th decimal spot? As I said before, *ignore* it, and do *not* round up the 4th decimal place to '5'! Post the 4 decimal spots just as they are.

I'm sorry if I'm making this seem more confusing. It's just that I was taught to round up to the next highest number, if the one that follows is 5 or more. That would be the wrong thing to do, in this case.

Ugh, now *I'm* frustrated! (Where's a 'screaming' smiley, when you need one?)
Do *not* read if you don't want the answer to enter, completely handed to you!
Spoiler (Rollover to View):
2.5854 is the answer to enter

_________________
E=MC˛
Energy (Power) = Mind Candy's Cube
PerplexCityTrades - Hunting4Treasure

PostPosted: Thu Apr 27, 2006 12:36 pm
Last edited by Hunting4Treasure on Thu Apr 27, 2006 1:14 pm; edited 2 times in total
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Fuseunderground
Decorated

Joined: 17 Dec 2005
Posts: 151
Hunting4Treasure wrote:
I was just trying to help others avoid a wasted wrong entry. Confused


Fair Enough, but you don't have that problem if you use the correct value for Pi.
_________________
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 12:48 pm
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Hunting4Treasure
Unfettered


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

 		Fuse,
I edited my post... Which value did you use? Confused
_________________
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Energy (Power) = Mind Candy's Cube
PerplexCityTrades - Hunting4Treasure

PostPosted: Thu Apr 27, 2006 1:05 pm
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Fuseunderground
Decorated

Joined: 17 Dec 2005
Posts: 151

 		I used the value for Pi in the nearest calculator
which was 3.14159265

This gave: [Warning includes answer]

Spoiler (Rollover to View):

6.684507609 then square root:
gives 2.58544147274
Rounded gives 2.5854


You are rounding correctly (over 5 go up etc.)
but you are not using an accurate enough value for Pi.
_________________
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 1:17 pm
Last edited by Fuseunderground on Thu Apr 27, 2006 1:27 pm; edited 1 time in total
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Hunting4Treasure
Unfettered


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

 		OK, that makes perfect sense! But, how would anyone automatically know to extend Pi by 8 places? I liked Sarah's example because the card asks for the answer to go 4 decimal places. It made sense to have Pi go 4 decimal places, too.

I'm not trying to be difficult, I'm just trying to understand your logic. Wink

BTW, I used my Windows Accessories calculator, if that makes any difference. Razz
_________________
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Energy (Power) = Mind Candy's Cube
PerplexCityTrades - Hunting4Treasure

PostPosted: Thu Apr 27, 2006 1:26 pm
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