GATE 2026 EE – 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 ______.
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Correct answer: (B) 4
Explanation
Write ON as 1 and OFF as 0. Initial: 0001000. Step 1: 0011100. Step 2: 0110110. Step 3: the end bulbs turn ON, giving 1110111. Step 4: the second and sixth bulbs (both neighbours ON) turn OFF, giving 1010101. In this state every OFF bulb has two ON neighbours and every ON bulb has OFF neighbours, so no rule applies and the state stays 1010101 in all later steps. At the end of Step 8, 4 bulbs are ON.