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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Black Puzzle Cards
[SOLVED] #217 Black Pixel Upper Left - Tower of Cubes
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aleph13
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Joined: 02 Mar 2005
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 		[SOLVED] #217 Black Pixel Upper Left - Tower of Cubes
Perplex City is home to many strange groups and organizations; perhaps none stranger than the Brotherhood of the Six, who revere and venerate the Cube. In the centre of their temple, in the heart of the old city, is a structure they call the "Tower of Cubes". It consists of 3 poles and 36 cubes of diminishing size, each with a hole through the centre.

At the beginning of time, so it is said, all the cubes were arranged in perfect order on the first, black pole. It is the duty of the Brotherhood to transfer all the cubes so that they sit, in perfect order, on the final, white pole. Various rules govern this holy activity. A larger cube can never sit on top of a smaller one, and only one cube may be transferred at one time; it is not permitted to hold a cube in one's hand, or to place it anywhere other than one of the poles.

According to ancient prophecy, when the cubes are all arranged on the white pole, the universe will be aligned in perfect harmony and there will be an end to all sorrow and grief. If one cube is transferred every minute, how long will it take for this blissful state of affairs to come to pass?

---------

Card by Gamet? Jamet?

55 Perplex Points

---------

On the bottom left of the image, there's three signs (like you'd see at a demonstration) with the words "Join Us! brotherhoodofthesix.com"

There would be a pic of the back (Map of the Radian Library area), but my camera's batteries died. Mad Soon, if someone else doesn't beat me to it.

[edit] Added camera pic of back.

[edit]Changed both images - Both are now scans. Note: the grey bar I added, to mask my number, since I scratched the silver off. Razz
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PostPosted: Sat Jul 16, 2005 5:33 am
Last edited by aleph13 on Mon Jul 18, 2005 7:02 am; edited 2 times in total
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tanner
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 		its just the tower of hanoi

So the formula for finding the number of minutes it takes to transfer 36 cubes from post A to post B is:.
Spoiler (Rollover to View):
2^36 - 1


EDIT
edited twice to fix spelling and spoilerise
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PostPosted: Sat Jul 16, 2005 5:49 am
Last edited by tanner on Sat Jul 16, 2005 11:11 am; edited 2 times in total
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aleph13
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 		It's a variation of the "Hanoi Tower" puzzle, or the "End of the World" puzzle. Those used 64, though.

For this puzzle, it should be 2 to the 36th power, -1 (number of minutes).

That's 68,719,476,735 moves, or minutes.

1,145,324,612 hours.

47,721,858.84 days.

6,817,408.406 weeks (approx)

131,104.0078 years (approx)

Please double check my math, but I think that's right. Very Happy
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PostPosted: Sat Jul 16, 2005 5:50 am
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tanner
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 		damn you just beat my edit Smile

so i wont bother Smile

you gotta be so damned quick!
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PostPosted: Sat Jul 16, 2005 5:54 am
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tanner
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 		given -- If one cube is transferred every minute, how long will it take for this blissful state of affairs to come to pass?

i think the solve is
Spoiler (Rollover to View):
2^36 - 1 minutes.


as i said

no need for days weeks or years
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PostPosted: Sat Jul 16, 2005 11:09 am
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aleph13
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 		I just added a camera pic of the back.

Sorry about the delay, but I'm having a hell of a time with my scanner. Once I've got that, I'll post scans, for much better images.
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PostPosted: Sun Jul 17, 2005 10:40 pm
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aleph13
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 		Okay! After completely reinstalling a 126 MB download of scanner software three times, it's functioning like it should.

And, I've updated the images above to both be the better-quality scans, instead of camera pics.
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PostPosted: Mon Jul 18, 2005 7:05 am
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spugmeistress
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 		nice that you've solved it n everything with the handy bit of math, but for the curious among us (or maybe just me) can anyone explain why it works? or the actual process - transferring the blocks to the rods in the right order n that? or if you cant be bothered, and it seems to be a well known puzzle, a handy web page explaining it would also suffice!

rach =)

PostPosted: Mon Jul 18, 2005 1:27 pm
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oliverkeers13
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 		Sure. Here's a site that has an explanation and a version so you can try it yourself. Good Luck.
http://www.cut-the-knot.org/recurrence/hanoi.shtml
*edit* forgot to add the link!
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PostPosted: Mon Jul 18, 2005 1:35 pm
Last edited by oliverkeers13 on Mon Jul 18, 2005 2:12 pm; edited 1 time in total
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toongoon
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 		I'm with Spugmeistress on this one. Also, I believe you neglected the link above - or is this another IE vs Firefox issue Wink

PostPosted: Mon Jul 18, 2005 1:41 pm
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tanner
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spugmeistress wrote:
nice that you've solved it n everything with the handy bit of math, but for the curious among us (or maybe just me) can anyone explain why it works? or the actual process - transferring the blocks to the rods in the right order n that? or if you cant be bothered, and it seems to be a well known puzzle, a handy web page explaining it would also suffice!

rach =)


using 3 cubes

123 / --- / ---
-23 / --- / --1
--3 / --2 / --1
--3 / -12 / ---
--- / -12 / --3
--1 / --2 / --3
--1 / --- / -23
--- / --- / 123

with just three discs/cubes
(2^3)-1 = 7 steps
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PostPosted: Mon Jul 18, 2005 1:48 pm
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oliverkeers13
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 		Just added the link
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PostPosted: Mon Jul 18, 2005 2:12 pm
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tanner
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 		mind you if they made a few mistakes it could take quite a bit longer Smile
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PostPosted: Mon Jul 18, 2005 3:00 pm
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Daffy889
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tanner wrote:
mind you if they made a few mistakes it could take quite a bit longer Smile


They wouldn't make mistakes! The holy Gyvann would help them to achieve a mystical one-ness with the holy object of the cube and get it right the first time!
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PostPosted: Mon Jul 18, 2005 3:36 pm
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cornflake
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 		Just for info, I'll post the link I found while looking for the answer. It's quite neat, as you can set it to have any number of discs.

http://members.shaw.ca/orionx/th/Hanoi.html?English

PostPosted: Fri Aug 05, 2005 11:49 am
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