# Bulbs in circle puzzle

On a circle there are 2014 light bulbs, 2 are ON, and 2012 are OFF.

You can choose any bulb and change the neighbor’s state i.e. * ON to OFF* or

*.*

**OFF to ON**Doing so,

What is the maximum number of bulbs we can turn on?

**ANSWER– **All the 2014 can be turned on

**EXPLANATION-
**

Let’s assume initial state of circuit as {**0,0,0,1,1,0,0,0,0…..,0,0**} where 1 = Switched ON & 0 = Switched OFF

Choose second last bulb from bulb which has state =1, then 2 bulb will be lighted on either sides

next state becomes {**1,0,1,1,1,1,0,1,0,0,0…..0,0**}

So, at each step we are lighting 4 bulbs, since 2012 is multiple of 4, there will come a stage where all bulbs will be ON.

I think it depends on the number of lightbulbs and the order the two lighted bulbs are in.

4 cases

1. If the two lighted bulbs are next to each other and the total number of lightbulbs is an odd multiple of 2 (odd # * 2), then we can turn on all bulbs.

2. If the two lighted bulbs are next to each other and the total number of lightbulbs is an even multiple of 2 (even # * 2), then we can turn on all but 2, **unless the total number of bulbs is 2, which doesn’t make sense here as a scenario anyways.

3. If the two lighted bulbs have a one bulb gap between them, and the total number of lightbulbs is an odd multiple of 2 (odd # *2), then we can turn on all but 2.

4. If the two lighted bulbs have a one bulb gap between them, and the total number of lightbulbs is an even multiple of 2 (even # * 2), then we can turn on all bulbs.

The two cases relevant here are case #2 and case #4. Try this for the simplest cases: 4 light bulbs and 6 light bulbs, and you’ll quickly see that these conclusions should hold true for larger sets.

One. Note that it says “change the neighbor’s state” NOT “neighbors’ stateS”. It does not say that changing state from 0-1 has an impact on the next neighbor to iterate.

The question in not clear enough. Because when sayin that: You can choose any bulb and change the neighbor’s state i.e. * ON to OFF* or

*does it mean that I must change both neighbors or can I choose to change only one of them? Also it is not clear if when asking “What is the maximum number of bulbs we can turn on?” means also how many will stay turned on or only how many can be turned on?*

**OFF to ON,**Lets check all the cases:

If we **must** change the state of both the neighbors than we have 3 cases

1) the bulbs are next to each other like **001100 **than we can light all the bulbs but only 2 will stay on

2) If there is a gap of one between the 2 bulbs like **010100 **than we can light all the bulbs but only 4 will stay on

3) If the gap is greater than 2 all the bulbs can be light but only 6 will stay on

If we don’t have to change the state of all the neighbors than we can light all the bulbs and all of them will stay on.

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »