[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Alfredo Cruz
Hello guys: I have been thinking half hr or so on this problem, so pls forgive me for anything wrong but I think I have an idea that might help: -Assuming: 1) Giving the nature of the number of colors I supposed that both the inner and outer disks are divided into an even number of pieces (n)

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Alfredo Cruz
Hello guys: I have been thinking half hr or so on this problem, so pls forgive me for anything wrong but I think I have an idea that might help: -Assuming: 1) Giving the nature of the number of colors I supposed that both the inner and outer disks are divided into an even number of pieces (n)

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Alfredo Cruz
Hello guys: I have been thinking half hr or so on this problem, so pls forgive me for anything wrong but I think I have an idea that might help: -Assuming: 1) Giving the nature of the number of colors I supposed that both the inner and outer disks are divided into an even number of pieces (n)

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Prunthaban Kanthakumar
On 3/25/07, Rajiv Mathews [EMAIL PROTECTED] wrote: On 3/25/07, Prunthaban Kanthakumar [EMAIL PROTECTED] wrote: If you see carefully his proof does not assume anything about sections colored continuously. His proof assumes only one thing Half of them are red and half of them are white

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Prunthaban Kanthakumar
Ouch I got the question completely wrong assuming the inner disc is continuous.Sorry for the confusion. On 3/25/07, Prunthaban Kanthakumar [EMAIL PROTECTED] wrote: On 3/25/07, Rajiv Mathews [EMAIL PROTECTED] wrote: On 3/25/07, Prunthaban Kanthakumar [EMAIL PROTECTED] wrote: If you

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Vishal
I did assume that the outer disk is painted half (contiguous) red and half white. However the 'equivalence' should do the trick and the same proof applies. As far as Stone's proof goes, I did not understand - For each inner section,no matter white or black ,there is 100 color-matching

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Santhosh Suresh
@Vishal When you rotate the inner section through it's 200 configurations, each of the inner section happens to come in tune with each of the outer sections, so there will 100 'matchings' and 100 mismatches. On 3/25/07, Vishal [EMAIL PROTECTED] wrote: I did assume that the outer disk is painted

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Prunthaban Kanthakumar
When both disks are not painted continuous 'equivalence' does not work. Because in your proof when one half does not give the answer, you just take take the other half and align it. But for arbitrary configuration, when one configuration does not work, you cannot align the other half. It will not

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Karthik Singaram L
@alfredo: I dint get this part: 1) Lets say that we have the outer circle painted in the following manner: 1 red(C1), 1 white(C2), 1 red(C3), etc. We call this sections (RWR) 2) Then if we have that the inner circle is painted in the same way we finish. 3) if not then lets say that we have a

[algogeeks] Re: traverse the tree layer by layer.

2007-03-25 Thread Lego Haryanto
That's a breadth first search. The only gotcha is that the usage of push and pop maybe misleading (implying that we're using stack). But actually it should use FIFO. You should view each push as enqueue and pop as dequeue. It will traverse the tree layer by layer, left to right. On 3/24/07, vim

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Alfredo Cruz
@Karthik I think the confusion arises from my lack of explanation in the nature of the pseudo-induction Lets take 2 sections in the outer circle that are painted red (S1, S2). My variable m messures the number of whites between S1 and S2 with no red sections. What I wrote is the basis of the

[algogeeks] Re: Pigeon Hole Principle

2007-03-25 Thread Vishal
Got it. Stone's solution seems to be right. On 3/25/07, Prunthaban Kanthakumar [EMAIL PROTECTED] wrote: When both disks are not painted continuous 'equivalence' does not work. Because in your proof when one half does not give the answer, you just take take the other half and align it. But for