The Light Bulb problem
There are 10 bulbs in a room, which are all initially switched off. There are also 10 people at the entrance of the room who enter the room one by one.
The first person switches every bulb on.
Next, the 2nd person toggles the state of every 2nd bulb. (2nd, 4th, 6th…..)
Next, the 3rd person then toggles the state of every 3rd bulb.(3rd, 6th, ….)
……. and so on.
When all the 10 people have finished walking through the room, what will be the state of each bulb? Which of the bulbs will be on/off?
It would be great if you can share your thought process as well.
Extension: What if there were 20 bulbs and 20 people? or 100bulbs and 100 people? Which of the bulbs would be finally on? How would you go about solving it?
Note: Try to work on this problem as if you were hearing it for the 1st time, from the eyes of a 10 yr old child.
What students worked out3
Student 19
I started out drawing the bulbs out and going through the process of canceling them out (if they were off).
While it was manageable for 1-10, I knew I couldn’t do it for 100, or even 30 bulbs because the process would be too cumbersome. So then I started picking individual numbers to try and understand the numbers at which they would be on or off.
Eg- 6: 1 (on), 2(off), 3(on), 6(off)
This led me to figuring out that I could use factors to understand where each number would be.
Then I tried to understand if the process can be made faster for 100. I realised that numbers with odd no. of factors would remain on, and numbers with even number of factors would remain off.
Still trying to understand if this can be made even more efficient (is there another pattern?)
Student 23
+1 to Aksika, started with drawing and still identifying the pattern…
Student 24
I was pretty much confused when I tried till only 5, but later on when I did a brute force thing till 10. I got the idea that it should be related to that logic of two states. The bulb has only two states either on or off. So I noticed if you go to a bulb twice it will be on then off again same applies if you go to bulb thrice it will be off, so similarly if you go to a bulb even number of times it will be off and ( taking the initial state as off), similarly if you go thrice it will be on ( again considering the initial state as off). based on this logic after 10th person visit. bulb 1, 4, and 10 will be on.