Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?
Show Hint
Mentally tile each candidate three times and check the seams for a broken or duplicated cell cluster; note: a close pixel level comparison of the four option images against the given strip in this pass matched pattern R (option C) more closely than pattern Q (option B), so this pairing may be worth a manual re check against the original PDF figure, though the answer below follows the official key's choice of Q (option B).
Here a single small square tile is repeated left to right to build the longer strip shown in the question, and only one of the four candidate tiles reproduces that exact strip, including at the seams where one copy meets the next.
The working method is to place two copies of a candidate tile side by side and check whether the black and white cells at the right edge of the first copy continue smoothly into the left edge of the second copy, with no notch appearing twice, no gap opening up, and no part of the motif getting flipped by mistake. A tile can look plausible on its own and still fail this seam check, which is what makes the four choices look deceptively close to each other.
P: on close inspection this tile does not carry its cell pattern through cleanly across the join.
Q: this is the tile identified by the official answer key as reproducing the strip when repeated.
R: looks close at a glance, and in fact lines up very well against the given strip, which makes it the tile most easily confused with the correct one.
S: has a similar overall density of black cells, but its internal notches do not all line up with the given figure once tiled.
Following the official key, the pattern that generates the figure is Q, option (B).
