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        riddles >> medium >>  one thousand rooms
        
(Message started by: tony123 on Nov 24^th, 2007, 11:15am)

Title: one thousand rooms
Post by tony123 on Nov 24^th, 2007, 11:15am

There are one thousand rooms in the sultan's palace. In each room there is a switch that switches all the lamps in the room on or off. When the lamps were on in each room and the sultan was bored, he walked through all his rooms one by one and repeated his walk again and again, always starting with the first room. During the first walk, he turned all the switches. The second time he turned the switch in every second room. The third time he turned the switch in every third room, and so on. (He turned the light on if it was off, and he turned it off if it was on). When he had walked through his room 500 times, he got tired of the game and decided to go to bed. He needed a room in which the lights were off. Which rooms did he have to choose from?

Title: Re: one thousand rooms
Post by gotit on Nov 24^th, 2007, 12:25pm

I think [hide]1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441 and 484.[/hide]

Title: Re: one thousand rooms
Post by cool_joh on Nov 24^th, 2007, 7:18pm

What was the initial condition? I think we can't solve it without knowing the initial condition.

Title: Re: one thousand rooms
Post by FiBsTeR on Nov 24^th, 2007, 8:23pm

on 11/24/07 at 19:18:03, cool_joh wrote:

What was the initial condition?

on 11/24/07 at 11:15:40, tony123 wrote:

[...] When the lamps were on in each room [...]

Title: Re: one thousand rooms
Post by cool_joh on Nov 24^th, 2007, 9:45pm

on 11/24/07 at 20:23:05, FiBsTeR wrote:

Oops, lol! :-[

So, I think Gotit is correct!

Title: Re: one thousand rooms
Post by Barukh on Nov 24^th, 2007, 11:24pm

Maybe I am missing something, but I don't understand gotit's answer.

What about room number 503?

Title: Re: one thousand rooms
Post by Grimbal on Nov 25^th, 2007, 6:03am

I also think the sultan was a bit lazy.

If he stopped after 500 turns, then all room over 500 except 529, 576, 625, 676, 729, 784, 841, 900, 961 would be dark.

Side notes:
Frankly, after turning 6569 switches, can't he just enter a room at random and switch off the light if necessary?
And what kind of sultan would enter a dark room, put on his pajamas and go to bed witout turning the light on?

Title: Re: one thousand rooms
Post by ThudanBlunder on Nov 25^th, 2007, 6:13am

on 11/25/07 at 06:03:49, Grimbal wrote:

And what kind of sultan would enter a dark room, put on his pajamas and go to bed witout turning the light on?

Depends what his wife looks like.

Title: Re: one thousand rooms
Post by gotit on Nov 25^th, 2007, 11:38am

on 11/25/07 at 06:03:49, Grimbal wrote:

I also think the sultan was a bit lazy.

If he stopped after 500 turns, then all room over 500 except 529, 576, 625, 676, 729, 784, 841, 900, 961 would be dark.

Yup. You are right. I missed that part. :P
So, the final solution is: all perfect squares less than 500 and all numbers greater than 500 that are not perfect squares.

Title: Re: one thousand rooms
Post by inquisitive on Dec 5^th, 2007, 1:03am

Can anybody explain how to get to the answer (except for writing a C program :) )

Title: Re: one thousand rooms
Post by Grimbal on Dec 5^th, 2007, 3:34am

Well, there is Java, VB, C#, ...

OK, well.

The point is to realize that the end state of a door depends on the number of divisors of the door number. And the number of divisors is odd only for perfect squares.

Title: Re: one thousand rooms
Post by Hippo on Dec 5^th, 2007, 4:34am

See http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1107492595

Title: Re: one thousand rooms
Post by temporary on Jan 27^th, 2008, 7:42pm

Correct me if I'm wrong, but [hide]Every perfect square from 1-500 or every non perfect square from 501 to 1000.[/hide]

Title: Re: one thousand rooms
Post by mikedagr8 on Jan 27^th, 2008, 7:44pm

on 01/27/08 at 19:42:51, temporary wrote:

Correct me if I'm wrong, but [hide]Every perfect square from 1-500 or every non perfect square from 501 to 1000.[/hide]

Quote:

So, the final solution is: all perfect squares less than 500 and all numbers greater than 500 that are not perfect squares.

Title: Re: one thousand rooms
Post by temporary on Jan 27^th, 2008, 7:49pm

A comment with no comment, just quotes is not very informative, no offense. Anyway, so we both got the right answer?

Title: Re: one thousand rooms
Post by mikedagr8 on Jan 27^th, 2008, 7:51pm

on 01/27/08 at 19:49:13, temporary wrote:

A comment with no comment, just quotes is not very informative, no offense. Anyway, so we both got the right answer?

Not informative? If you view this forum from afar, you should be able to do a few basic things. I provided you with the results that you asked for. Correct me if I am wrong. I never stated you were wrong, I was allowing you to see something. Open your eyes to the world if you will.

Title: Re: one thousand rooms
Post by temporary on Jan 27^th, 2008, 7:58pm

I already knew he posted that. I saw it right after posting my answer. If i would look at the answer before answering, it would be pointless to answer because I would not be doing it myself.