Question

Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?

• A. P
• B. Q
• C. R
• D. S

Hint:

Find the one or two cells where P, Q, R, and S actually differ from each other, then check only those spots against the given figure.

Answer 1

The Correct Option is B

Step 1: Understand what generating the figure means.
The wide strip at the top is built by taking one small square tile and repeating it side by side (and sometimes mirroring it) across the width of the strip. Only one of the four candidate tiles P, Q, R, S, when repeated this way, reproduces the strip exactly, cell for cell.

Step 2: Break the strip into tile-sized blocks.
Since each candidate tile is a square made of small black and white unit cells, mark the top strip off into consecutive blocks the same width as one tile. Each block should look identical, allowing for the mirrored copies a repeating tile naturally produces, if the strip really was generated from a single tile.

Step 3: Compare each block of the strip against the four candidates, cell by cell.
Look at the small distinguishing features: the exact position of a corner notch, the step where a black arm bends, and the row holding a lone white cell, in each candidate. Patterns P and R differ from the strip in the position of the top-right step, and S differs from the strip in one middle cell. Pattern Q is the only one whose cell arrangement lines up with every repeated block of the strip without a single mismatched cell.

Step 4: Confirm by checking the joins between repeated tiles.
Where two repeated copies of the generating tile meet in the strip, the pattern must continue smoothly with no broken line. This edge-matching test also singles out Q, since assembling copies of P, R, or S at these joins leaves a visibly broken or offset line, while copies of Q join up cleanly.

Final Answer:
The strip is generated from pattern Q. \[ \boxed{\text{Q}} \]