There is man named 'Mabu' who switches on-off the lights along a corridor at our
university. Every bulb has its own 'toggle' switch that changes the state of the light. If the light is off, pressing the switch turns it on. Pressing it again will turn it off.
Initially each bulb is off.
He does a peculiar thing. If there are 'n' bulbs in the corridor, he walks along the corridor back and forth 'n' times. On the 'i'th walk, he toggles only the switches whose position is divisible by 'i'.
He does not press any switch when coming back to his initial position.
The 'i'th walk is defined as going down the corridor (doing his peculiar thing) and coming back again.
Assume n=44,100.
Determine the final state of the last (44,100th) bulb. Is it on or off?
off ??
ReplyDeleteThis comment has been removed by the author.
ReplyDelete44,100th bulb is surely off.
ReplyDeleteP.S.: I solved a similar puzzle with friends about an year ago.. so this one seemed easy..
Here's the one we faced earlier:
In the same problem as anuj bhaiya posted, suppose n=100. Find out how many bulbs are finally in the 'on' state.
Try it.. I have the answer(with logic).
This comment has been removed by a blog administrator.
ReplyDeleteoh yes m sorry.. :P
ReplyDeleteit shud be on..(a bit calculation mistake!)
hats off Siddharth..
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteno one posts the solution. not yet.
ReplyDeletein the first case (n=44)the bulb will be off
ReplyDeletewhile in the second case it will be on
m i correct ???
@prashant
ReplyDeleten = 44100 ,
not 44 and 100
@anuj bhiaya
i'll take care of that in future bhaiya.
wow, after a long time i found an easy problem here
ReplyDeleteShivanker, about your question,
ReplyDeleteanswer 10 right?
for general value of n, [sqrt(n)] will be the answer as only perfect squares will satisfy this.
Thanks bhaiya,pehli baar aapse hats off mila!
ReplyDelete