There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, …). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, …). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?
2006-07-11 20:19:46 · 20 answers · asked by 42ITUS™ 7 in Entertainment & Music ➔ Jokes & Riddles
That was no guess, igloo. Time for 42ITUS to bow before the better riddler.
*Bowing*
We're not worthy!
It took me forever to figure out I had to factor the numbers!
2006-07-11 20:32:22 · update #1
on
10
2006-07-11 20:24:57 · answer #1 · answered by iamigloo 6 · 2⤊ 0⤋
The number of times the bulb is switched is the number of ways two numbers can multiply to give a certain number. For example...
1 x 18 = 18
18 x 1 = 18
2 x 9 = 18
9 x 2 = 18
3 x 6 = 18
6 x 3 = 18
Notice that these come in pairs, with one exception: if a number is a perfect square, there will be an unpaired "a x a" in the middle. In that case, the light bulb will be turned on only once, not twice. So bulbs that are perfect squares will remain lit at the end.
2006-07-12 10:20:39 · answer #2 · answered by Polymath 5 · 0⤊ 0⤋
Number 64 is on, as are all of the square numbered light bulbs (1, 4, 9, 16, 25, 36, 49, 64, 81 and 100)
2006-07-11 20:28:56 · answer #3 · answered by Mags 2 · 0⤊ 0⤋
64
2006-07-11 22:50:07 · answer #4 · answered by OrangeApple 5 · 0⤊ 0⤋
If the first one already switch on every bulb , there will be no more bulb for others to flip on ?
So all the bulb should be on isn't it?
so answer should be all on
2006-07-11 22:04:00 · answer #5 · answered by petleo67 2 · 0⤊ 0⤋
#64 is on and so is all the other perfect square numbered light bulbs so 10 are on
2006-07-11 20:27:36 · answer #6 · answered by theuntouchablejdub 3 · 0⤊ 0⤋
64th bulb is ON. The bulbs will be like this:
[1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
where 0 is OFF, and 1 is ON.
2006-07-11 20:35:18 · answer #7 · answered by arkiso 2 · 0⤊ 0⤋
This woman needs to step up and tell this guy to hit the line. that's not your position to bypass and strive against like an animal for a lady. If she should be with him so be it. there are multiple females accessible who will be your woman without each and each and every of the drama. What the hell, i will't stand wimpy chicks like that. i ought to by no potential enable some guy to reason drama with my guy.
2016-11-06 06:10:04 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Don't normally do this but, I read all the answers first, they are all so very good - I haven't a chance for the "best answer", therefore, won't even try - - It's a good "riddle", however, a little too long for "cocktail party" banter, wouldn't try it!!!! Did you take "math" in college?
2006-07-12 04:56:18 · answer #9 · answered by Anonymous · 0⤊ 0⤋
2 points!
2006-07-11 21:52:24 · answer #10 · answered by police 6 · 0⤊ 0⤋
I think I hear an electrical storm in the distance.
2006-07-11 20:43:38 · answer #11 · answered by bankster 3 · 0⤊ 0⤋