Concept:Periodic rotational sequence patterns repeat after a fixed modular period \(T\); the orientation at step \(N\) is given by \(N \pmod T\).
Formula / Rule / Reaction:$$\text{Periodic Index} = N \pmod T \quad (T = 4)$$
Solution:- The arrow rotates 90 degrees clockwise in a 4-step cycle: Box 1 (Up), Box 2 (Right), Box 3 (Down), Box 4 (Left).
- For Box 12: \(12 \pmod 4 = 0\), which corresponds to the 4th position in the cycle (pointing Left).
- Thus, Box 12 matches Image 4 (Option D).
Why other options are incorrect:- Option A (Image 1): Points Up, corresponding to \(N \equiv 1 \pmod 4\) (Boxes 1, 5, 9).
- Option B (Image 2): Points Right, corresponding to \(N \equiv 2 \pmod 4\) (Boxes 2, 6, 10).
- Option C (Image 3): Points Down, corresponding to \(N \equiv 3 \pmod 4\) (Boxes 3, 7, 11).
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