| # Worked example (K=3, T=6) | |
| ## Prompt | |
| ``` | |
| 3 cells sit in a ring (c1..c3, and c3 is adjacent to c1). Initial values: c1=6, c2=6, c3=0. | |
| Each step, every cell SIMULTANEOUSLY becomes the sum modulo 10 of its two ring neighbours (left and right). Apply this for 6 steps. Only AFTER your thinking, you will be asked for one cell's final value -- answer with ONLY that value as \boxed{d} (a single digit). | |
| Reason inside <think> </think> -- after each step write all 3 cell values in order c1..c3. | |
| ``` | |
| ## Hidden CA evolution (each row c_t carried by ONE soft token z_t) | |
| c_0 (initial): [6, 6, 0] | |
| c_1 (after step 1): [6, 6, 2] | |
| c_2 (after step 2): [8, 8, 2] | |
| c_3 (after step 3): [0, 0, 6] | |
| c_4 (after step 4): [6, 6, 0] | |
| c_5 (after step 5): [6, 6, 2] | |
| c_6 (after step 6): [8, 8, 2] | |
| ## Query | |
| Final value of cell c2: -> 8 | |