Correct Option (1)
The sequence of figures follows a repeating two-step operational pattern:
- Operation 1: All shaded and unshaded beads are interchanged (colors are inverted).
- Operation 2: The columns of the figure are interchanged.
Let's analyze the progression of the given figures:
- Figure 1 to Figure 2: Figure 1 (Shaded-Unshaded / Unshaded-Shaded) undergoes Operation 1 (invert colors) to become Figure 2 (Unshaded-Shaded / Shaded-Unshaded).
- Figure 2 to Figure 3: Figure 2 (Unshaded-Shaded / Shaded-Unshaded) undergoes Operation 2 (swap columns) to become Figure 3 (Shaded-Unshaded / Unshaded-Shaded).
- Figure 3 to Figure 4: Figure 3 (Shaded-Unshaded / Unshaded-Shaded) undergoes Operation 1 (invert colors) to become Figure 4 (Unshaded-Shaded / Shaded-Unshaded).
Following this established alternating sequence of operations, the transition from Figure 4 to the fifth figure should involve Operation 2 (swap columns).
- Figure 4 to Figure 5: Applying Operation 2 (swap columns) to Figure 4 (Unshaded-Shaded / Unshaded-Shaded) means the first column (Unshaded / Shaded) moves to the right, and the second column (Shaded / Unshaded) moves to the left. This results in the figure (Shaded-Unshaded / Unshaded-Shaded).
This derived figure matches the configuration presented in Option 1.
Incorrect Options:
Options 2, 3, and 4 do not represent the correct fifth figure in the sequence. Option 2 (Unshaded-Shaded / Shaded-Unshaded) is identical to Figure 4, which would imply no change in the sequence, contrary to the established pattern of transformations. Options 3 and 4 depict different arrangements of shaded and unshaded beads that do not conform to the alternating pattern of color inversion and column swapping derived from the preceding figures.
