# Light all the bulbs — Puzzle for Interview rounds

# Question :

Consider a circle with

2014 light bulbs and only 2 of them are on and the rest are off. Anyone can choose any of the bulbs and change the state of the neighboring bulbs. The task is to find if we can switch all the 2014 light bulbs on ?

# Solution :

Yes, it is possible to get all the light bulbs **ON**.

- Firstly label all the 2014 light bulbs from
**B-1**to**B-2014**(in sequence). - As the positions of the light bulbs in the
**ON**state are not mentioned in the problem statement. - So, consider that those 2 bulbs are adjacent to each other and are labeled
**B-1**and**B-2**. - Therefore, bulbs labeled from
**B-3**to**B-2014**are initially in the**OFF**state and all the bulbs in the**OFF**state are adjacent to each other.

Follow the steps below to solve the given problem:

- Consider all the
**2012 remaining bulbs**in groups of**4**.

2. In order to light up all the bulbs perform the following strategy:

- The first group consists of bulbs
**B-3**to**B-6**. - Select the second bulb from the chosen group and change the state of adjacent bulbs.
- Here, select bulb
**B-4**and change the state of bulbs**B-3**and**B-5**from the**OFF**state to the**ON**state. - The second step is to select a third bulb from the chosen group and change the state of its adjacent bulbs.
- Here, select the bulb
**B-5**and change the state of bulbs**B-4**and**B-6**from**OFF**to**ON**.

3. Similarly, the above process can be repeated for a total of **503** groups(consisting of 4 light bulbs each) and all the given **2014** light bulbs can lighten up.