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Light All the Bulbs | Puzzles for Interview - Interview Preparation PDF Download
Introduction
Imagine a circle with 2014 light bulbs, and only 2 of them are on, while the rest are off. You can pick any bulb and change the state of its neighboring bulbs. Can you figure out how to switch all the 2014 light bulbs on?
Labeling the Light Bulbs
To solve this problem, we need to label all the light bulbs from B-1 to B-2014. As the positions of the two bulbs that are already on are not mentioned in the problem statement, we can assume that they are adjacent to each other and labeled B-1 and B-2. Therefore, bulbs labeled from B-3 to B-2014 are initially off, and all the off bulbs are adjacent to each other.
Strategy to Switch on All 2014 Light Bulbs:
To light up all the bulbs, we need to follow these steps:
- Step 1: Group the remaining 2012 bulbs into groups of four.
- Step 2: Select the second bulb from each group and change the state of its adjacent bulbs.
- Step 3: Select the third bulb from each group and change the state of its adjacent bulbs.
For example, the first group of bulbs consists of B-3, B-4, B-5, and B-6. We select B-4 as the second bulb and change the state of B-3 and B-5 from off to on. Then, we select B-5 as the third bulb and change the state of B-4 and B-6 from off to on. We can repeat this process for the remaining 502 groups of bulbs, and all the 2014 light bulbs will be switched on.
Conclusion
In conclusion, it is possible to switch on all 2014 light bulbs by using the above strategy. By grouping the bulbs and changing the state of their adjacent bulbs, we can light up all the bulbs and solve the problem.
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Dec 28, 2024 Last updated |
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