GATE 2026 CE (CE1) – Question 9
Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (B) 4
Explanation
Following the rules step by step, the bulbs ON (numbered 1 to 7) are: initially 4; after Step 1: 3, 4, 5; after Step 2: 2, 3, 5, 6; after Step 3: 1, 2, 3, 5, 6, 7; after Step 4: 1, 3, 5, 7. In Step 5 each OFF bulb has two ON neighbours, so none turns on, and each ON bulb has OFF neighbours, so none turns off. The pattern 1, 3, 5, 7 stays the same, so 4 bulbs are ON at the end of Step 8.