How Many Lightbulbs Will Remain Turned On?

  • Thread starter Thread starter nabliat5
  • Start date Start date
  • Tags Tags
    Lightbulb
AI Thread Summary
In a scenario with 1,000 light bulbs and 1,000 students, each student toggles the state of specific bulbs based on their student number. The first student turns all bulbs on, while subsequent students toggle bulbs at intervals corresponding to their student number. The key discussion point revolves around determining how many bulbs remain lit after all students have completed their actions. The final conclusion indicates that 50 bulbs will remain turned on. This outcome is derived from the pattern of toggling, which relates to the number of divisors each bulb number has, ultimately leading to the realization that only bulbs corresponding to perfect squares will stay on.
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..)
 
Physics news on Phys.org
uhm...50.
 
Just ONCE, I wanted to see a post titled Status Update that was not a blatant, annoying spam post by a new member. So here it is. Today was a good day here in Northern Wisconsin. Fall colors are here, no mosquitos, no deer flies, and mild temperature, so my morning run was unusually nice. Only two meetings today, and both went well. The deer that was road killed just down the road two weeks ago is now fully decomposed, so no more smell. Somebody has a spike buck skull for their...
Thread 'RIP George F. Smoot III (1945-2025)'
https://en.wikipedia.org/wiki/George_Smoot https://physics.berkeley.edu/people/faculty/george-smoot-iii https://apc.u-paris.fr/fr/memory-george-fitzgerald-smoot-iii https://elements.lbl.gov/news/honoring-the-legacy-of-george-smoot/ https://www.nobelprize.org/prizes/physics/2006/smoot/facts/ https://www.aps.org/publications/apsnews/200611/nobel.cfm https://inspirehep.net/authors/988263 Structure in the COBE Differential Microwave Radiometer First-Year Maps (Astrophysical Journal...

Similar threads

Replies
2
Views
4K
Replies
4
Views
5K
Replies
18
Views
2K
Replies
3
Views
2K
Replies
698
Views
113K
Replies
14
Views
2K
Replies
7
Views
5K
Back
Top