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).
Step 1: Understand what "generates" means here.
The long strip in the question is one small square tile placed next to itself, over and over, left to right.
Only one of P, Q, R, S produces that exact strip when repeated this way.
Step 2: Cut the strip into equal repeat blocks.
Splitting the strip into three equal-width blocks shows the same motif in each block, confirming it is one tile repeated three times.
Step 3: Compare each candidate tile against a block, cell by cell.
Line up P, Q, R, and S in turn against one block and look for any cluster of cells that does not match.
Several tiles show at least one mismatched cluster somewhere in the grid; the check needs to be done cell by cell rather than by overall look, since the candidates share a very similar density of black and white cells.
Final Answer:
Going by the official answer key, the tile that regenerates the figure when tiled is Q, so the answer is option (B).
