Can you solve this picture puzzle and fill in the black areas?

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Discussion Overview

The discussion revolves around solving a picture puzzle that involves filling in black areas of an image. Participants explore various interpretations and solutions related to the color patterns in the puzzle, which is linked to a multiplication table for integers mod 7. The scope includes conceptual reasoning and mathematical patterns.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the solution involves a rainbow pattern shifting colors down each row.
  • Others propose specific color arrangements based on the multiplication table for integers mod 7, associating colors with numerical values.
  • A participant mentions the necessity of including red blocks in the solution, indicating they are integral to the image.
  • Several participants share their own solutions and express difficulty in viewing images due to permission issues on the hosting site.
  • One participant describes a method for constructing their solution based on the colors and their relationships, emphasizing the importance of the red border in the pattern.
  • Another participant outlines a perceived pattern in the columns of colors, suggesting a systematic approach to filling in the puzzle.
  • Some participants express confusion about the patterns and request explanations from others, indicating varying levels of understanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single solution or pattern, as multiple competing views and interpretations of the puzzle remain throughout the discussion.

Contextual Notes

Some participants mention limitations in accessing images, which may affect their ability to fully engage with the proposed solutions. Additionally, the complexity of the patterns discussed suggests that there may be multiple valid approaches to solving the puzzle.

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Perhaps a Rainbow shifting its colors every row down
 
I believe this might be what you were going for? Can't put it in white... it's an image :P [Attached]
 

Attachments

  • coloredsquare.gif
    coloredsquare.gif
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I don't think you can attach images in this forum--at least, I can't view it. It says I do not have permission to access the page. Put it on ImageShack. (http://www.imageshack.us/, you don't even have to register)
 
Huh, now I am seeing it. Anyway, nope, that's not it.

By the way, the red blocks on the top and left are a necessary part of the image, although yours is not correct even if you add them back in.
 
Last edited:
This was interesting. I found a few solutions; but this is the one I liked most and thought was most probable.

My solution
 
DaveC426913 said:
My solution.

I can't see this one or the other one posted. I'm getting the same error BicycleTree was getting about permissions. Do you know what that is?
 
It didn't work for me until I clicked "log out" on the permission denied page and then it showed a small thumbnail.
 
  • #10
You got it, Dave! But can you explain it?
 
  • #12
Rahmuss said:
This was interesting. I found a few solutions; but this is the one I liked most and thought was most probable.

My solution
Mind explaining that one? I can't figure out what your pattern is though it looks like you had something in mind.
 
  • #13
Okay, time to explain the puzzle:

The puzzle is the multiplication table for the integers mod 7. Red = 0, orange = 1, yellow = 2, green = 3, blue = 4, indigo = 5, violet = 6.

Alternatively, you can think of it like this: sampling from the colors ROYGBIV in order, so that on the first line each square is the same color as the previous square, on the second line each square is one color cycled ahead from the previous square, on the third line each square is two colors cycled ahead from the previous square, and so on down to each square is six colors cycled ahead from the previous square on line 7.
 
  • #14
BicycleTree said:
Mind explaining that one? I can't figure out what your pattern is though it looks like you had something in mind.

Sure!

I figured that the red was actually part of the pattern, not just part of the border for the image. So I realized that the next inner loop (after the multicolored one) also has two sides (top and left side) which were not defined. So, since the top and left side of the bigger portion were red, I added that as a border there. Then I constructed it like the outer multi-colored design... that is... I took what color was in one corner and put it also in the other corner... also with the one next to the corner I put next to that same corner on the other side. Then to find what other color was missing I took the relation between the two given colors (orange and lavender) and realized that going from right to left going back two spaces it goes from orange to lavendar to green. Thus I used Green as my last color for that layer. Then the only other logical color for the middle would be red as it is part of the pattern. I actually did another one similar to the one that Dave posted; but not quite the same.
 
  • #15
I see how Dave got his... at least in my own mind. Take the column to the left (right of the red column) it has a pattern.
1st Column: Orange, Yellow, Green, Blue, Lavander, Pink.
2nd Column: Yellow (skip 1), blue (skip 1), Pink (skip 1 - red in this case), Orange (skip 1), Green (skip 1), Lavander.
3rd Column: Green (skip 2), Pink (skip 2), Yellow... etc...
4th Column: Blue (skip 3), Orange (skip 3), Lavander (skip 3) ... etc...
... etc...

Does that make sense?
 
  • #16
Okay on your first post--not the simplest pattern, I'd say, though.

Yes, for your second post--I also posted an alternative explanation (post # 13).
 
  • #17
BicycleTree said:
Okay on your first post--not the simplest pattern, I'd say, though.

Yes, for your second post--I also posted an alternative explanation (post # 13).

Not the simplest pattern, no; but my brain doesn't always like the simple things. :biggrin: I tend to over-complicate things when I think it's going to be quite complex.
 

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