Question

Shown on the left are three tiles. Which option(s) can be made using only these tiles? Rotations of tiles are allowed. 

• A. A
• B. B
• C. C
• D. D

Hint:

When working with tiles, visualize the possible rotations and arrangements that form the desired shape without exceeding the available shapes.

Answer 1

The Correct Option is B, D

Step 1: Analyze the shape and arrangement of tiles. By rotating the tiles, the shapes in options B and D can be constructed from the available tiles.
Step 2: Option A and C cannot be formed since they require additional tiles or different shapes that are not available.
Step 3: Therefore, the correct answers are (B) and (D).

Answer 2

The base tile shown on the left is a single column split into three parts: a plain square top, a curved leaf-like middle section, and a quarter-circle tapering to a point at the bottom. Since rotations of this tile are allowed, four copies of it, turned to different angles, are combined to build each 2x2 answer pattern. The tile only fits cleanly against a rotated copy of itself when a curved edge meets another curved edge of matching direction, or a straight edge meets another straight edge; a curve meeting a straight edge, or two curves bulging the same way instead of nesting into each other, leaves a mismatch.

1. Option A: In this arrangement, one of the curved leaf edges is left facing a plain straight edge from the neighbouring tile instead of nesting into a matching curve, leaving a visible mismatch in the pattern.
2. Option B: Here, every curved edge of the tile faces a matching curved edge from a neighbouring rotated copy, so the leaf shapes combine into complete closed curves, such as the small full circle formed where two quarter-circle edges meet, and the straight edges likewise line up cleanly with other straight edges.
3. Option C: In this pattern, two of the tile's curves bulge toward each other the same way rather than nesting into one another, which leaves a gap rather than a clean fit.
4. Option D: This pattern also leaves one curved section unmatched against a straight section from its neighbour, breaking the otherwise repeating pattern.

Only option B keeps every curved and straight edge matched cleanly across all four rotated copies of the tile, with no leftover gaps or mismatched edges anywhere in the 2x2 arrangement.

So the option that can be made using only the given tile is Option B.