In an exceptionally long corridor in the Virtupets Space Station, there are one thousand windows along one wall. Coincidentally, there are exactly one thousand Grundos in the station. Dr Sloth orders the first Grundo to open the blinds on every window. Then, he orders the second Grundo to close the blinds on every second window. Then the third Grundo is told to go to every third window, and close the blinds if they are open, and open the blinds if they are closed. The fourth Grundo does this for every fourth window, and so on.
2007-02-28 10:28:48 · 7 answers · asked by queen_gemini1 1 in Science & Mathematics ➔ Astronomy & Space
Here's a website with a similar problem you can go to for a better description, but i'll try to explain it for you. First, you get the number of factors per number. if a number has an even number of factors, it will end up closed, but if it has an odd number of factors, it will be open. so, the only windows that will be left open are the ones that are in a position represented by a perfect square: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.
2007-02-28 10:37:38 · answer #1 · answered by stephieSD 7 · 0⤊ 0⤋
Oh, this one is cute. Let every window be numbered from 1 to 1,000 in sequence. If a window of a number N has an even number of distinct divisors besides 1, then it will be left open. Otherwise, if N has an odd number of distinct divisors besides 1, it's left closed. Now for any N, break it down into its prime factors at powers a, b, c, d, etc..
N = 2^a * 3^b * 5^c * 7^d * ...
The number of distinct factors N may have besides 1 is
(a+1)(b+1)(c+1)(d+1)... -1.
The only way this number can be even is if (a+1), (b+1), (c+1), (d+1), ... are all odd. That means a, b, c, d, ... etc, are all even, and thus N is a perfect square.
Only windows numbered by perfect squares will be left open, all the rest will be closed.
2007-02-28 19:10:12 · answer #2 · answered by Scythian1950 7 · 0⤊ 0⤋
I know Grundos are very obedient,so you can be sure they did what they were told.
I just wondered when they finish do they have to start over,
2007-03-01 07:51:54 · answer #3 · answered by Billy Butthead 7 · 0⤊ 0⤋
ok here, this is the identical problem, just replacing grundos with students and blinds with lockers....and everything's mentioned, method and solution....check it out....
here's the link:
http://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.72342.html
2007-03-02 13:46:59 · answer #4 · answered by sxyniknoit 1 · 0⤊ 0⤋
What's the question?
2007-02-28 18:31:54 · answer #5 · answered by es_harper2007 2 · 0⤊ 0⤋
well whats the problem? It seems senseless action, but why not!
2007-02-28 18:33:22 · answer #6 · answered by Matiss S 1 · 0⤊ 0⤋
is there a question here?
2007-02-28 18:33:55 · answer #7 · answered by Anonymous · 0⤊ 0⤋