Question

Below are two patterns created by repetition of circles. For each pattern, identify the base configuration (1–7) from which it has been tiled. Which statement is/are TRUE? 

• A. I can be created from 3 and 4; and II can be created from 5 and 6
• B. I can be created from 1 and 2; and II can be created from 5, 6 and 7
• C. I can be created from 4; and II can be created from 6
• D. I can be created from 4 and 5; and II can be created from 6 and 7

Hint:

Match the neighbour directions: if only N–S–E–W overlaps appear, look for a cross unit; if diagonals also appear, the seed must include diagonal neighbours.

Answer 1

The Correct Option is C

Identify Pattern I (left).
The tiling shows a square grid where each circle overlaps exactly with its four orthogonal neighbours, giving a ``clover'' at each grid point.
This arises from repeating the four-around-one cross unit (configuration 4) on a square lattice—no diagonals are needed.
[4pt] Identify Pattern II (right).
Here, every grid point shows a star/rosette made by orthogonal and diagonal overlaps; each circle meets 8 neighbours (N, S, E, W, and the four diagonals).
This requires the denser rosette seed where one circle is surrounded so that diagonals are included—configuration 6.
Therefore I $⇒$ 4 and II $⇒$ 6, which matches option (C).
\[ \boxed{\text{I from 4; II from 6}} \]