A very hard riddle (i hope)

[mandiehun]

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 2nd bulb(turning off bulbs,2,4,6....) Person NO.3 enters and flips the switch on every 3rd bulb(changing the state on bulbs 3,6,9...) This continues untill 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 had passed through the room?

 

[gcol]

You need to get out more mate.

 

[mandiehun]

Your absolutely right i do

 

[securespark]

You said last time that would be the last.....

I got to light bulb 3 having drawn it all out on a multi-coloured chart.

Unfortunately, I was using white-board markers and got high on the fumes......who cares how many light bulbs are on, man, as long as they are CFL's?

 

[mandiehun]

now now, do u's really have to have an attitude, its only a bit of fun, if u dont want to do the riddle then dont And i know i said the last one would be the last one but they were too easy. I wont post any more

 

[toasty]

Who will operate each bulb is the best way of looking at it, I think.

Obviously person number 2 will do all the even numbers when they come into the room, and (say) person number 5 will operate all the bulbs that end in a five or zero.


So who would operate for example bulb 24? :

Persons numbered: 1 & 24, 2 & 12, 3 & 8, 4 & 6 ........ (i.e on, off, on, off, on, off, on, off) so bulb 24 ends up off

That is all the factors (numbers by which 24 is divisible) will be in pairs. This means that for every person who switches a bulb on there will be someone else to switch it off. This willl result in the bulb being back at it's original state. (i.e off)

So why aren't all the bulbs off?

Think of bulb 36:-

The factors are: 1 & 36, 2 & 13, 6 & 6

Well in this case whilst all the factors are in pairs the number 6 is paired with it's self. Clearly the sixth person will only flick the bulb once and so the pairs don't cancel. This is true of all the square numbers.

So for bulb 64:

Persons numbered: 1 & 64, 2 & 32, 4 & 16, 8 & 8 ........

i.e it would get left on as would all sqare numbered bulbs, there are 10 square numbers between 1 and 100 (1, 4, 9, 16, 25, 36, 49, 64, 81 & 100) hence the 10 bulbs that are square numbers remain on.

Nice question BTW

 

[Thermo]

nice answer toasty, but it would only take two postings of off or on to get the right answer!

 

[securespark]

now now, do u's really have to have an attitude, its only a bit of fun, if u dont want to do the riddle then dont And i know i said the last one would be the last one but they were too easy. I wont post any more

It wasn't an attitude! Tch! Do I have to end every jokey comment with a " ", to show I'm joking?

 

[Richardp]

64%1=0 - ON
64%2=0 - OFF
64%4=0 - ON
64%8=0 - OFF
64%16=0 - ON
64%32=0 - OFF
64%64=0 - ON
So, light #64 is On.

There are 10 perfect sqaures between 1 and 100:
1,4,9,16,25,36,49,64 (hence it's on), 81, 100

 

[Richardp]

Mr. Moody grumbles about bad time-keeping trains from morning till night!. On one particular morning he was quiet justified. His train left on time for the one hour journey, to Clarksville, and it arrived 5 minutes late. However, Mr. Moody 's watch showed it to be 3 minutes early, so he adjusted his watch by putting it forward 3 minutes. His watch kept time during the day, and on the return journey in the evening the train started on time, according to his watch, and arrived on time, according to the station clock. If the train travelled 25 percent faster on the return journey than it did on the morning journey, was the station clock fast or slow, and by how much?

 

[bethrob99]

9 mins fast?

 

[Doc Lenny]

9 mins fast?

/3=answer

 

[Richardp]

The station clock is 3 minutes fast. The morning journey took 65 minutes, and the evening journey therefore took 52 minutes, and the train arrived 57 minutes after it should have left, that is, 3 minutes early.

 

[securespark]

Was he listening to the Monkees?