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 Forum index » Archive » Archive: Perplex City » PXC: Puzzles
Scarlett's Granier Painting Puzzle
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thalamus
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Joined: 10 Mar 2006
Posts: 111
Location: Edinburgh, Scotland, UK

 		i tried getting everything matched up - hoping to colour each 'corner' of the cube a single colour ...

(see pic)

...before i realised that each corner only needs 3 squares and there are 4 of each colour - doh

however - that led me to think that maybe we need to get a cube where no two squares of the same colour are touching, as brienigma mentioned above.

from the way the pic is laid out, i imagine the cube to be made of two interlocking pieces: one piece consists of top, frontleft, and frontright faces and the other piece is made up of base, backleft and backright.

combine this with the 2 fixed squares...

does this help nudge anyone's brain towards a solution ?
1.jpg
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PostPosted: Tue Sep 05, 2006 12:26 pm
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StarryNight
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Joined: 16 Dec 2004
Posts: 90
Location: New Hampshire

 		I took a different take on this and came up with the following solution, which I've emailed to Scarlett. I wish I had access to a graphics program and more time right now, but I don't, so I've had to write it out in text. If someone could post a graphic of what this would look like, that would be great!

Spoiler (Rollover to View):
Short description:

• Turn the block on the upper right side 90 degrees counter clockwise
• Turn the block on the bottom 180 degrees

Long description:
Ignoring the background completely and looking only at the six blocks, the goal is to ensure two constraints: 1) No colors should be adjacent to each other and 2) one instance of each color should be facing inward, toward the lighthouse.

Contraint 1:

The top block has 2 squares that face the upper left block – the squares on the left and at the bottom. The upper left block has 2 squares that face the upper block – the squares on the top and the right. These four colors must be different

The upper left block has 3 squares that face the lower left block – the squares on the left, bottom and right. The lower left block has 3 squares that face the upper left block – the squares on the left, top and right. These six colors must be different.

The lower left block has 2 squares that face the lower block – the squares on the bottom and the right. The lower block has 2 squares that face the lower left block – the squares on the left and the top. These four colors must be different.

The lower block has 2 squares that face the lower right block – the squares on the top and the right. The lower right block has 2 squares that face the lower block – the squares on the left and the bottom. These four colors must be different.

The upper right block has 3 squares that face the lower right block – the squares on the left, bottom and right. The lower right block has 3 squares that face the upper right block – the squares on the left, top and right. These six colors must be different.

The top block has 2 squares that face the upper right block – the squares on the right and at the bottom. The upper right block has 2 squares that face the upper block – the squares on the top and the left. These four colors must be different

Constraint 2:

These six colors must be different:

The square at the bottom of the upper block
The square at the right of the upper left block
The square at the right of the lower left block
The square at the top of the lower block
The square at the left of the lower right block
The square at the left of the upper right block

The only configuration that satisfies all of these constraints is the above solution.

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PostPosted: Tue Sep 05, 2006 2:14 pm
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thalamus
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Joined: 10 Mar 2006
Posts: 111
Location: Edinburgh, Scotland, UK
StarryNight wrote:
I took a different take on this and came up with the following solution, which I've emailed to Scarlett. I wish I had access to a graphics program and more time right now, but I don't, so I've had to write it out in text. If someone could post a graphic of what this would look like, that would be great!



you can use this tool to see how it looks

http://stuff.perplexcitymap.com/mosaic.htm

why did you decide on those particular constraints ?

PostPosted: Tue Sep 05, 2006 2:23 pm
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StarryNight
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Joined: 16 Dec 2004
Posts: 90
Location: New Hampshire
thalamus wrote:

you can use this tool to see how it looks

http://stuff.perplexcitymap.com/mosaic.htm

why did you decide on those particular constraints ?


ActiveX controls are blocked where I am right now. I'll have to look at that later.

I chose these constraints with the idea of not having adjacent colors overlap - ie, colors facing an adjacent block. I chose that strategy after mapping out the colors and looking at the pattern of the colors that were missing in each block.

When I worked through the possible solutions that would satisfy that constraint, there were 2 possible solutions and one of those had all different colors in the "inside six" positions, which seems like a logical puzzle goal.
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PostPosted: Tue Sep 05, 2006 2:46 pm
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hobyrne
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 		Alternate cube
Sylvia wrote:
Don't know if this makes any since, but try this.
I can't explain it, but maybe you will know what i mean.
It creates a pattern when 2 (2X2) are put side by side.

Oh and 1 should say 12.


Some simple ASCII graphics:

Rotating the puzzle 1/8 revolution counterclockwise, it can be represented thus:

Code:

   xxxxBB
 AAxxxxBBx
 AA      xx
xx        CC
xx        CC
xx        xx
xx        xx
FF        xx
FF        xx
 xx      DD
  xEExxxxDD
   EExxxx


Noting that a block of A is directly above a block of F, a block of B is directly to the right of a block of A, but B to C is diagonal and F to E is diagonal, etc., the pairs of 3 tiles 'joined together' look something like:

Code:

   BB
 AABB
 AA
FF    CC
FF    CC
     DD
   EEDD
   EE


If you 'fold' the FAB block, you get half of a cube:


Code:

   +--+
   | B|
   | B|
+--+--+--+
|  |AA|BB|
|FF|AA|  |
+--+--+--+
   |F |
   |F |
   +--+
   |  |
   |  |
   +--+


So, the CDE will fold into half a cube too, and they'll fit together.

Someone take it from here? My mind is fizzing.

PostPosted: Tue Sep 05, 2006 5:33 pm
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Sylvia
I Have No Life

Joined: 21 Apr 2006
Posts: 2062

 		Maybe this will explain better than before. And since I can't get the images to display in the order I want them to, I will make 3 post to explain my weird thinking.

First, is the original image with the unnecessary background removed and the 6 colors labeled A,B,C,D,E,F, for easier comparison and their numerical position.
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PostPosted: Tue Sep 05, 2006 9:08 pm
Last edited by Sylvia on Fri Sep 22, 2006 1:36 pm; edited 1 time in total
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Sylvia
I Have No Life

Joined: 21 Apr 2006
Posts: 2062

 		Next is my weird thinking on how to make a cube considering 12 and 8 can't be moved.
So if visualize a cube 12 would be the top and 8 would be the front and 6 would be the bottom. While 10 would be the left side and 4 the right side and 2 the back.

Since 12 and 8 can't be moved they create the first pattern top to bottom with 6 and 2 reversing the pattern.
Then going across 10 and 8 create the first pattern with 4 and 2 reversing the pattern.

This may not be right, but it just has to be close.
mosaic_Cm.jpg
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PostPosted: Tue Sep 05, 2006 9:15 pm
Last edited by Sylvia on Fri Sep 22, 2006 1:37 pm; edited 1 time in total
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Sylvia
I Have No Life

Joined: 21 Apr 2006
Posts: 2062

 		And the final product. I hope this helps and doesn't confuse. But more than that, I hope it helps to solve the puzzle so you can move forward.
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PostPosted: Tue Sep 05, 2006 9:20 pm
Last edited by Sylvia on Fri Sep 22, 2006 1:37 pm; edited 1 time in total
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cruse4
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Joined: 14 Mar 2006
Posts: 83
Location: Plymouth, England

 		Don't know if this has been mentioned yet, but the lighthouse from the picture features in card 160 - Fingerprints. It can be seen on a bottle of wine in the card, the bottle reads "Chateau Vucetich" with the number 231 under it...then in small print there is "...(something which i can't make out) cellars".

Thought i'd mention it incase it helps in some obscure way! Laughing
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PostPosted: Tue Sep 05, 2006 10:00 pm
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hobyrne
Guest
Sylvia wrote:
Next is my weird thinking on how to make a cube considering 12 and 8 can't be moved.
So if visualize a cube 12 would be the top and 8 would be the front and 6 would be the bottom. While 10 would be the left side and 4 the right side and 2 the back.

Since 12 and 8 can't be moved they create the first pattern top to bottom with 6 and 2 reversing the pattern.
Then going across 10 and 8 create the first pattern with 4 and 2 reversing the pattern.

This may not be right, but it just has to be close.


Ahaa, I see now what you mean. The 'antipode' of each square is the same colour as it is.

But what makes you think 10 and 4 are
Code:

ED -- FC
FC -- ED

and not
Code:

FE -- CD
CD -- FE

or the 2 other rotations?

PostPosted: Tue Sep 05, 2006 10:33 pm
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Sylvia
I Have No Life

Joined: 21 Apr 2006
Posts: 2062

 		hobyrne, I don't know. I'm just throwing it out here. That's what I'm good at. You guys will have to actually solve it. And it could be another way, but this should give a good starting point, if it is not the actual solve.

PostPosted: Tue Sep 05, 2006 11:16 pm
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poozle
Entrenched

Joined: 15 Aug 2005
Posts: 1090

 		Just remember the top and bottom ones can't be moved (was mentioned in scarletts latest update Wink)

PostPosted: Wed Sep 06, 2006 5:14 am
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sylvastriker
Greenhorn

Joined: 18 Aug 2006
Posts: 7

 		I think that Starrynight has the right solution, I look forward to seeing what she says in response to his email. I came to the same solution this morning. thought this may help Strarrnight's ideas

Spoiler (Rollover to View):
assuming each raised part has a point going either N E S W for direction. There is 6 colours and each raised square has one free point facing away from the central picture. I wanted to be able to have a different colour on each external point ie.

12 N, 2 E, 4 E, 6 S, 8 W, 10 W.

So if you go with spinning

2 90degrees Anticlockwise
6 180 degrees either direction

This means that all facing out are different colours, also all facing in are different colours.

My final point is that as you go move clockwise round the picture each piece has the previous pieces external colour next to it, illustrating which piece is coming next.

For example

the colour on 2 E is on 4 S
the colour on 4 E is on 6 W
the colour on 6 S is on 8 N
and so on. all the way round

this also works for the in inside pointing parts


PostPosted: Wed Sep 06, 2006 5:56 am
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doublecross
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Joined: 25 Jul 2005
Posts: 588
Location: London, UK

 		Poozle, not top and bottom, but top, and bottom left (i.e. 12 and 8 o'clock)
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xx

PostPosted: Wed Sep 06, 2006 6:09 am
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GreenWindmill
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Joined: 21 Apr 2006
Posts: 195
Location: Midlands, UK

 		I'm still intrigued by the Rubik's cube style theory. It fits with the cube theme running throughout many of these puzzles and also has a retro feel which I think was implied in one of Scarlett's messages.

My small thought was that maybe the pieces need to be placed in order to form a 'solvable' cube. This would require the cube to have no two colours adjacent on corners because that would render it unsolvable, I think it would also require each colour to be paired on 'joins' with four of the other colours once and not at all with the remaining colour.

That makes sense in my head but I can't seem to get it coherent when I put it in print! If anyone has the faintest idea what I'm trying to say and sees any value in it then please take it forward, my tiny brain can't wrap itself around the problem sufficiently to follow this through.

Of course, the problem with all of the solutions we're looking at currently is that we're having to make assumptions about how the tiles would form a cube. If we're wrong about which piece is on top, which on the back, etc. presumably that throws solutions out? Or am I missing something? Can't see a way around this but nobody seems to be worrying about it for some reason!

Sorry - hadn't intended to post this long, especially since I haven't added a whole lot to the discussion!
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PostPosted: Wed Sep 06, 2006 6:29 am
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