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

In summary, the puzzle is the multiplication table for the integers mod 7. The pattern is found by creating a design based on 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.
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  • #2
Perhaps a Rainbow shifting its colors every row down
 
  • #3
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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  • #4
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)
 
  • #5
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:
  • #7
This was interesting. I found a few solutions; but this is the one I liked most and thought was most probable.

My solution
 
  • #8
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?
 
  • #9
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.
 

1. What is the purpose of a picture puzzle?

A picture puzzle is a type of game or activity that requires you to use your problem-solving skills to complete a picture by filling in the missing pieces. It can help improve cognitive abilities such as spatial reasoning, memory, and attention to detail.

2. How do you solve a picture puzzle?

The first step in solving a picture puzzle is to observe the image and identify any patterns or clues that may help you fill in the missing areas. Then, you can start with the edges and work your way towards the center, using trial and error to find the right piece for each spot.

3. Are there any specific strategies for solving picture puzzles?

There are various strategies that can be used to solve picture puzzles, such as sorting the pieces by color or shape, starting with the most distinct areas of the image, or using the image on the box as a reference. Ultimately, the best strategy will depend on the individual and the complexity of the puzzle.

4. Is solving picture puzzles beneficial for the brain?

Yes, solving picture puzzles has been shown to have numerous benefits for the brain. It can improve cognitive skills, problem-solving abilities, and can even help prevent age-related cognitive decline. It also provides a fun and engaging way to exercise the brain.

5. Can picture puzzles be used for scientific research?

Yes, picture puzzles can be used as a tool in scientific research. They can be used to study cognitive abilities, such as visual perception and problem-solving, and to develop and test new strategies for solving puzzles. They can also be used in educational settings to study learning and memory processes.

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