Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #126 20051231 03:57:24
Re: Very interesting problems..How about a chain of length 1? Or 0, even. Why did the vector cross the road? It wanted to be normal. #127 20051231 04:31:56
Re: Very interesting problems..Yes, but actually length =0 and length=1 are trivial. IPBLE: Increasing Performance By Lowering Expectations. #128 20051231 04:41:43#129 20051231 04:44:10#130 20051231 05:15:08
Re: Very interesting problems..So the problem is mathematical, not programmical. IPBLE: Increasing Performance By Lowering Expectations. #131 20051231 05:27:22
Re: Very interesting problems..Let start. IPBLE: Increasing Performance By Lowering Expectations. #132 20051231 05:35:01
Re: Very interesting problems..How old are you Seerj IPBLE: Increasing Performance By Lowering Expectations. #133 20051231 05:39:40
Re: Very interesting problems..When you have the proof please don't post it immediately. I want to test myself. IPBLE: Increasing Performance By Lowering Expectations. #134 20051231 06:05:34
Re: Very interesting problems..I got interesting results. But first I have to define a function: is the smallest perfect square greater than n. We have that sq↑[x]>x. Let sq↑[sq↑[sq↑[...sq↑[x]]]]=sq↑n[x] Last edited by krassi_holmz (20051231 06:45:11) IPBLE: Increasing Performance By Lowering Expectations. #135 20051231 06:24:03
Re: Very interesting problems..I followed your logic until you said "But we have igloo myrtilles fourmis #136 20051231 06:26:11
Re: Very interesting problems..John, i' explain later. IPBLE: Increasing Performance By Lowering Expectations. #137 20051231 06:41:44
Re: Very interesting problems..How to produce ">" in LaTeX? IPBLE: Increasing Performance By Lowering Expectations. #138 20051231 06:49:45
Re: Very interesting problems..Let look at the neightbours of n in chain with length n amd maxNumber n: n+x > n+y => Let Then so So when there does not exist chain with Length n and MaxNumber n. From the upper equation we get: => => for 0 ≤ n < 5.8 there doesn't exist that kind of chain, so n>5. Last edited by krassi_holmz (20060103 04:26:36) IPBLE: Increasing Performance By Lowering Expectations. #139 20060103 04:30:02
Re: Very interesting problems..I generalized my first result: IPBLE: Increasing Performance By Lowering Expectations. #140 20060103 05:08:45
Re: Very interesting problems..Here is it: is the left neigtbour of number i and is the right neightbour of i. Then the sums and must be perfect squares, so: 1. If then and So generally <<  (1) 2. When we get the same as (1) ,so (1) is for all i<n (n=CH.length) Now to summarize ner[i] and nei[i]: So But, from (1) follows: So if n is "squarible" we must have ; I used a computer program to compute the first members and for n<14 all are negative, so n>13 Last edited by krassi_holmz (20060103 05:39:47) IPBLE: Increasing Performance By Lowering Expectations. #141 20060103 06:30:24
Re: Very interesting problems..
Yes, this does mean intersection. IPBLE: Increasing Performance By Lowering Expectations. #142 20060107 23:39:05
Re: Very interesting problems..my friend is winning the contest ..He's the only person who shown why 32 is the minimum number. #143 20060108 02:00:14
Re: Very interesting problems..Please, seerj, tell us how did he done it. IPBLE: Increasing Performance By Lowering Expectations. #144 20060108 02:03:25
Re: Very interesting problems..I'l try full logic examination program. It will proof that 32 is the minimal, but it will be very slow. IPBLE: Increasing Performance By Lowering Expectations. #145 20060108 05:41:31
Re: Very interesting problems..I'm doing the same Krassi. I had it done before, but I realized that a method I used to cut down on execution time just eliminated some needed tests. So I'm back to my original program. It takes O(n!) time, right now it's on size 12 and has to do 479,001,600 comparisons. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #146 20060108 05:53:53
Re: Very interesting problems..Hah! I am so stupid... Last edited by Ricky (20060108 05:56:22) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #147 20060108 06:45:13
Re: Very interesting problems..Give some program code. IPBLE: Increasing Performance By Lowering Expectations. #148 20060108 06:58:37
Re: Very interesting problems..Alright, here is the psuedo code: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #149 20060108 07:03:13
Re: Very interesting problems..C++ code: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #150 20060108 07:07:01
Re: Very interesting problems..Oh, and as a note, for each combination it will find two lists. For example, it will find: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 