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Black and White Square Box puzzle

My buddy and I have been trying to figured out how to solve this puzzle sent to us by a professor several weeks back. All we've been asked to answer is, "What do you think is the correct answer and why?". For some context, our professor is a mathematician who creates puzzles as exercise projects for our class to solve every semester. Each puzzle is different but are meant to apply the same abstract learning/pattern identification techniques to aid our learning.

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  • $\begingroup$ With six boxes arranged in that exact pattern, probably a good idea to try Braille first. $\endgroup$
    – Bass
    Nov 29, 2022 at 10:37
  • $\begingroup$ Does your professor normally present you with puzzles of this sort, or do the puzzles usually have a question mark somewhere? As given, there doesn't appear to be a question asked (apart from the 'what is the answer?' question). $\endgroup$ Nov 29, 2022 at 15:46
  • $\begingroup$ @IanMacDonald Not necessarily...there have been times where he asks if we've generally identified a pattern or will specifically ask for our methodology/thought process for determining our outcome. $\endgroup$
    – Julian
    Dec 1, 2022 at 7:44

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The pattern here is that

in each row, the white square is moving clockwise one step at a time; in each column, the red slash moves clockwise one step at a time.

If there's some additional "answer" they're looking for, I'm not sure what it could be.

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It's a bit of a leap in logic, although another potential answer if that if you treat each white square and red lined square such that...

...each represents a separate number. You can get to these tables fairly easily: enter image description here

Subsequently, if you divide the content of table A by the contents of table B you get the following sequence where the sequence of totals of each row and column match:

enter image description here

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  • $\begingroup$ Interesting idea, but you have a typo in your red line table. Bottom centre should be 3. $\endgroup$
    – fljx
    Nov 29, 2022 at 22:11
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A possible pattern is

That the red slashes occupy each cell in the inner left column twice each and the inner right column once each.

The white squares occupy the top right, middle left, and bottom right cells twice each, and the others once.

Overall this leaves the middle right cell as the only cell that is never occupied by the same thing twice. Furthermore outer top middle square is the only one where the red slash and white box occupy the same cell and it's the middle right cell.

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black regions are numbered in the puzzle

There are 9 black regions in the puzzle. I numbered them from 1 to 9 as shown above.

Each black region has 3X2 white bordered cells in them. One of the cell is having red slant line and another cell is filled with white color inside with some padding.

Now on quick wink, we can see that the entries in the cells changes their position from one region to another.

The “Red Line” moves clock wise in a cycle of 4steps - 3steps - 3steps (inclusive of current cell) The “White filled” cell moves clock wise in a cycle of 2steps - 2steps - 3steps ( Inclusive of current cell)

Journey of "Red Line Cell"

At first it was in the 2nd row - 1st column cell in the black region numbered as 1.

It took 4 Steps clockwise and landed in 2nd row - 2nd column in Second black region.

and then it moved 3 steps clockwise and landed in 3rd row - 1st column cell in 3rd black region.

From there it took 3 steps clockwise and landed in 1st row - 1st column cell in 4th numbered black region.

Thus it takes 4 steps - 3 steps - 3 steps

Journey of "White Filled Cell"

At first it was in 1st row - 2nd column cell in the black region numbered as 1. Then it started journey with 2 steps clockwise(inclusive of current cell) and landed in 2nd row - 2nd column cell in 2nd black region.

After that as per cycle, it took 2 steps clockwise (inclusive of current cell) and landed in 3rd row - 2nd column cell in the 3rd numbered black region.

As the next step in the cycle, then it took 3 steps clockwise(inclusive of current cell), it landed in 2nd row - 1st column cell in the 4rd numbered black region.

If we apply the same cycle repeatedly, remaining cells will be revealed.

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Top centre square is the correct answer. If we consider, each square as a 6*2 matrix the red slash and white shade lands on the following matrix indices.

Red slash

                    (2,1)(2,2)(3,1)
                    (1,1)(3,2)(2,1)
                    (1,2)(3,1)(1,1)

Index not visited twice - (2,2)(3,2)(1,2)

White shade

                    (1,2)(2,2)(3,2)
                    (2,1)(1,1)(1,2)
                    (3,2)(3,1)(2,1)

Index not visited twice - (2,2)(1,1)(3,1)

Index not visited twice that is common between red slash and white shade : (2,2)

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