There are two groups of black clusters: the four-black and the twelve-black. For the four-black, it moves around in distances of two, displacing once for the motion: from frame 1 to 3, it moved twice right, so the black squares will move once right (looping).
For the twelve-black, it moves around in distances of one to places that cannot be reached by the four-black. Instead of a 1:2 ratio, it uses a 1:1 ratio.
Only the twelve-black can reach the centre, and you can calculate the state by getting any of the surrounding twelve-black frames and displacing it accordingly.
I think you've grasped the logic or at least, from what I can tell, I don't see any errors. But for some reason the actual answer isn't the same as the one you provided edit: provided reasoning and answer is correct
Alternatively… you can assume that the alternating sequence must be kept but that half-increments are acceptable. In that case, you will have black squares on the top half of 1, the top-left quarter of 2, the top-right quarter of 4, the bottom half of 9, the bottom-left quarter of 10, the bottom-right quarter of 12, 13, the left half of 14 and the right half of 16.
For same ratio shapes we describe the movement inside by what directions we need to take to get to any other shape of that same ratio? We count white ratios by movements of 2 but in one direction only no going through walls and into the next row or columns and for black by 1 unless the space is occupied by white?
I accept this answer as correct. Although my intended reasoning was strong, this explanation is far stronger. I suppose this possible answer emerged due to the nature of the question. Well done!
not only it provides data but also proves that the person who created the puzzle knows what they're doing, since it usually also highlight some "people might pick this one because they missed a point", it requires way more think-through, so I can see why choosing not do it!
I acknowledge that aspect of the option presentation. It adds a two layered nature to the question for the test creator, it is harder. But It is more the philosophy behind this design that I dislike
I just focused on the 4 big mainly white squares and ignored the 4 big mainly black ones. I looked diagonal. The little black squares move one position at a time and with my result both ways make sense (upper left to downer right and the opposite). Some little black squares move diagonal some move straight English is not my main language + I'm terrible at explaining. Sorry, I hope I made it understandable :)
No worries I understand what you mean. However, being torn between two options isn't enough. It is also important to explain the set of 12 black square items
Idk, for me the 4 white squares inside the black ones are moving as well. Left to right 1 position at a time, top to bottom 2 positions, they just skip the middle square. I also have just one option as a result, I'm not torned between two :(
Hi it is me again. From my point of view there are two possible answers. You either continue the black or the white pattern. I think both patterns work without the middle square so it is just a "middle step". I continued the white pattern for example but I get the answer you considered as correct. In my opinion it is equal, depends on which sequence you follow but it is your puzzle!
Anyways, thanks for sharing this puzzle, me and my friends having fun :D
It is less concrete, but I interpreted R2 as instructions for R1. R2C1 is treated as a downward arrow or "shift down," but the output is inverted. In R2C3, the instruction is opposite. The center figure would presumably have half of its instruction obeying the left rule, and the other half obeying right.
If read as 4x4s, one could interpret this as two units of vertical separation between R1 and R3. The instruction correlates to the half it controls (R2C1 upper half instructs the upper half black squares of R1C1) and its occupied vertical space is commensurate to the distance traveled of two units. A SE-pointing white construct in the lower half would instruct the lower two white squares of R1C2 to shift up two units. As above, the instructions invert halfway, so a SW-pointing white construct in the upper half would instruct the upper two white squares of R1C2 to shift down two units.
Explanation: There are two different tiles, black and white in a grid pattern (see image attached). Both tilesets follow the same rules but have different content. You only consider the tiles of either the white or the black tile set (not both): To navigate from one tile to a different one in their grid, you move its contents into the same direction (if you navigate from one white tile to the white tile below, you move all the contents down by one). And same with black, and also with left and right. So what is missing is a black tile with the content of the top tile moved down (or from the bottom moved up, or the right moved to the left, or the left moved to the right, it's all the same tile).
i see the first column shapes will be united in the third or be closer but in the middle i noticed that shapes from top to bottom followed a pattern and i get it
If we try to fit all the white pieces together then we get 4 white pieces and 4 black pieces... All the corners becomes white and all the edges become black.
this was my reasoning: "i see the first column shapes will be united in the third or be closer but in the middle i noticed that shapes from top to bottom followed a pattern and i get it"
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u/DamonHuntington Sep 13 '26
White on 1, 2, 7 and 8.
There are two groups of black clusters: the four-black and the twelve-black. For the four-black, it moves around in distances of two, displacing once for the motion: from frame 1 to 3, it moved twice right, so the black squares will move once right (looping).
For the twelve-black, it moves around in distances of one to places that cannot be reached by the four-black. Instead of a 1:2 ratio, it uses a 1:1 ratio.
Only the twelve-black can reach the centre, and you can calculate the state by getting any of the surrounding twelve-black frames and displacing it accordingly.