Which Figure Completes the Sequence?

Explanation

Community Solutions We received many thoughtful responses to this puzzle. Several participants not only found the intended answer but also approached the pattern from different perspectives, tested alternative interpretations, and explained their reasoning in detail. Here are six community responses we found particularly valuable: 1. u/Mactucrus87_ Hi! This time i say E 1. the small square in the corners spin clockwise 2. the small square in the corners alternate between black and white 3. the polygons in the middle are always formed by 5 lines So this give us Solution E Edit: we can also try another algorithm. Let’s say that the figures in the top row have a match in the second row, and must have 2 things in common. The 1st figure match with A, they are the only ones that have a regular polygon (square and pentagon), and have a Black corner square. The third figure match with letter C, they are the only ones with a black square in the top right corner, so same color and same position of the corner square. Box 4 is connected with letter D, they both share that they are made by rectangles, AND share the fact that they both have the corner square that is white. Then we have box 5, it has in common with B and E the fact that is a Open figure, but only has in common with B the dark corner Square. So 5 goes with B. The only one that remains out is letter E which is the solution. Why we selected this response: Mactucrus87_ went beyond the straightforward solution. After identifying the clockwise movement, alternating color of the corner square, and five-line structure, they developed a second, independent matching method to test the same conclusion. Reaching E through two different approaches made this one of the most creative analyses we received. ⸻ 2. u/lemasney Thanks for the kind shout out! I believe the answer is E: There are two elements to consider in the puzzle at each frame. The white and black squares appear to be appearing alternatively in each frame, black, then white, then black, and so on. They appear to be showing up in opposite corners, black in lower left and upper right exclusively, and white in lower right and upper left exclusively. The black square in the last frame repeats the pattern. For this reason, I believe the white square would appear at the upper left in the missing frame. Meanwhile, the shifting shape in the center appears to contain 5 linear segments in each frame. They appear as both open and closed forms. D nearly meets the pattern, except that it has 6 linear segments, which does not fit the pattern. E has the white square in the correctly predicted corner, and has a shape that contain 5 linear segments. I’m not as sure as I usually am with your puzzles, but from the available solutions, it appears to be E. Why we selected this response: lemasney carefully followed both independent elements of the puzzle. The response predicts the position and color of the missing corner square, examines the five-segment structure, and then explicitly compares D with E before eliminating D. The step-by-step reasoning makes the solution particularly easy to follow. ⸻ 3. u/Square-Winter-3257 Its E. All we need is the corner squares and the line count. Mainly because to do it based on anything else is way overly complicated to the point of looking like its trying to look smart. But lets make up something that fits I guess: 1. When a outer square changes color, the angles used in the middle shape have to go between not 90 degrees, and 90 degrees. Therefore it can be anything but C. 2. There is no indication that a shape will be filled in, therefore it can’t be C, again. 3. Each shape has 5 lines, therefore it can only be B or E. 4. B and E are the same shape, but different rotations. So to solve if its B or E, based only on the middle shape, we need to figure out how the rotation works. 5. The first and 3rd shape appear to be the same rotation, however there also fairly similar (i.e. 1 is a regular pentagon, 3 is a concave pentagon) in that it could just be rotated to have an edge flat. 6. If based solely on just image 1 and 3, B makes the most sense. Though you could also just argue E, because E is technically flat down as well. 7. SO based on rotation, I dont think any of the shapes make any sense. Okay so We have B or E, rotation doesn’t help us. Neither B or E are a quadrilateral with a line in them. So if the rule was that if it’s a quadrilateral forming the outside of the shape, that the corner square is empty, then it’s more likely to be B. And at that I can’t think of anything that technically tells us it’s B or E, other than an educated guess that it’s E. But if I’m going to be pedantic, I personally can’t see a way the middle shape tells us anything to distinguish between B and E. But also im just being pedantic because i hate puzzles like this. Why we selected this response: Square-Winter-3257 did something particularly valuable: instead of stopping when a plausible pattern appeared, they tested whether that pattern actually determines the answer uniquely. Their observation that the five-line condition alone cannot distinguish B from E raises a legitimate ambiguity and adds a critical perspective to the discussion. Examining the limits of a proposed rule is just as valuable as finding the rule itself. ⸻ 4. u/SeparateBumblebee546 i’m thinking E! I was between D and E on account of the small boxes in the corners, it seemed like it should be a white box in the upper left corner, and then the object in the middle is also composed of 5 lines in all of them (i was a bit on the fence on the fifth one, but the lines do look like they’re 2 separate lines and not one long line). Why we selected this response: SeparateBumblebee546 identified both major clues and also highlighted one of the easiest details to overlook. The distinction between two separate line segments and what may initially appear to be one continuous line is important when counting the central figure. This makes the explanation particularly useful for anyone who hesitated between the available options. ⸻ 5. u/JeffTheNth All of them have a 5-line object in them, and a square in a corner The square in the corner appears to rotate clockwise, alternating filled and empty That would mean empty in the top-left corner, giving D or E D has a 6-line object, while E has a 5-line object, so I’d say E was the answer Why we selected this response: JeffTheNth provided one of the clearest elimination-based solutions. The corner square’s clockwise movement and alternating fill first narrow the possibilities to D and E. The line count is then used as the deciding condition. It is concise, structured, and very easy to follow. ⸻ 6. u/AdEmotional8815 D In my reasoning it could have only been D, or E; because the square in the corner moves clockwise to the other corners, and changes from black to white and vise versa every turn. From picture 1 to 3 you can also see a part of the geometric figure went missing, or got flipped. It’s not a 100% though, as that only restores the outlines and not the line in the middle of the figure in picture 3. On the other hand when you remove parts from the figure in image 3, or move parts around it won’t become the figure in picture E (at least in terms of the basic outlines. Edit: I just counted the number of straight lines of the figures, and if they are all supposed to be 5 lines, then I’m wrong and it’s E. Lol, dammit. Why we selected this response: What stood out here was the willingness to revisit an initial hypothesis. AdEmotional8815 correctly identified the clockwise movement and alternating color of the corner square, initially explored a more complex transformation rule, and then returned to the figures to test another property. After noticing the five-line pattern, they revised the original answer from D to E. This process of testing, reconsidering, and correcting a hypothesis is a valuable part of logical problem-solving. We also appreciate their continued participation and thoughtful contributions to our puzzles.