How Many Lightbulbs Will Remain Turned On?

  • Thread starter nabliat5
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In summary, if there are 1000 light bulbs in a room, each with a switch that can turn it on with one push and off with two pushes, and 1000 students enter the room and take turns pushing the buttons according to their number (i.e. student 1 pushes all buttons, student 2 pushes every second button, etc.), then 50 light bulbs will remain on after all 1000 students have pushed the buttons in this way.
  • #1
nabliat5
there is a 1000 light bulbs in a room
near each bulb there is a switch which turns the bulb near it on in a push of a button
and turns it off in a second push of a button and turns it on again in the third push of a button.

1000 students come into the room
the first student pushing every button once (thus turning every lighbulb on)
the second student pushes every second button (turned off every even place lightbulb)
the third student pushes every third button
etc..

how many lightbulbs will remain turned on
if all 1000 students will act the same way as before(the 4th will push every 4th button etc..)
 
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  • #3
uhm...50.
 

1. How is the number of remaining lightbulbs calculated?

The number of remaining lightbulbs is calculated by subtracting the number of burnt-out lightbulbs from the total number of lightbulbs.

2. What factors affect the number of remaining lightbulbs?

The number of remaining lightbulbs can be affected by factors such as the initial quality of the lightbulbs, the frequency and duration of use, and external factors like power fluctuations or temperature changes.

3. Is there a way to predict how many lightbulbs will remain turned on?

There is no definitive way to predict the exact number of lightbulbs that will remain turned on, as it depends on various factors and can vary in different situations. However, statistical analysis and mathematical models can be used to estimate the probability of lightbulbs remaining turned on.

4. How can the number of remaining lightbulbs be increased?

The number of remaining lightbulbs can be increased by using higher quality or more durable lightbulbs, reducing the frequency and duration of use, and ensuring stable power supply and suitable environmental conditions for the lightbulbs.

5. Can the number of remaining lightbulbs be affected by user behavior?

Yes, user behavior can play a role in the number of remaining lightbulbs. For example, turning off lights when not in use and handling lightbulbs properly can help prolong their lifespan and increase the number of remaining lightbulbs.

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