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

You are not logged in. #1 20051222 04:22:54
Very interesting problems..Hi all i'm new in this forum! [ And Happy Xmas Holidays!] #3 20051224 03:50:04
Re: Very interesting problems..I made program to try to solve it with brute force, but for even a list of size 20, it needs to build and test at least 10^20 different lists, since the function is O(n!). "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..." #4 20051224 05:48:53
Re: Very interesting problems..what means that the sum is perfect square? IPBLE: Increasing Performance By Lowering Expectations. #5 20051224 05:52:58
Re: Very interesting problems..√2, not perfect, not an integer. Heck, not even rational. "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..." #6 20051224 06:21:23
Re: Very interesting problems..Here are some analisys that may be helpful: IPBLE: Increasing Performance By Lowering Expectations. #7 20051224 06:40:49
Re: Very interesting problems.."The sum of all perfect squares is 2n(n+1)/2" Last edited by Ricky (20051224 06:42:26) "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..." #8 20051224 06:42:19
Re: Very interesting problems..The the remainder of the sum of every two consecutive numbers when it's divided by 4 must be 0 or 1. IPBLE: Increasing Performance By Lowering Expectations. #9 20051224 06:45:38
Re: Very interesting problems..
They don't have to be consecutive. You can arrange them in any order you want around a circle, and every two numbers that are next to each other have to add up to a perfect square. "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..." #10 20051224 06:51:07
Re: Very interesting problems..And for the Ricky's suggest that √2 is not even rational. Here's interesting theorem: IPBLE: Increasing Performance By Lowering Expectations. #12 20051224 10:07:43
Re: Very interesting problems..&& stands for the logic AND #14 20051224 10:29:04
Re: Very interesting problems..So somebody could write a program. IPBLE: Increasing Performance By Lowering Expectations. #15 20051224 10:36:17
Re: Very interesting problems..
It sure does, at least in computer science. But now apply that to:
It doesn't make sense.
Hold on. You said in your first post:
Doesn't that mean that 2, 4, 5, 7... 14 would also have to be in there? Last edited by Ricky (20051224 10:38:02) "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..." #16 20051224 10:41:02
Re: Very interesting problems..Here is ss with 7 numbers: IPBLE: Increasing Performance By Lowering Expectations. #17 20051224 10:46:01
Re: Very interesting problems..And here's ss with 13 numbers: IPBLE: Increasing Performance By Lowering Expectations. #18 20051224 11:05:44
Re: Very interesting problems..I modified my program so that it selects from a list of integers from 1 to 100 and creates lists: Last edited by Ricky (20051224 11:22:49) "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..." #19 20051224 11:10:03
Re: Very interesting problems..Here's an algoritm that creates infinite series: Last edited by krassi_holmz (20051224 11:16:44) IPBLE: Increasing Performance By Lowering Expectations. #20 20051224 11:15:29
Re: Very interesting problems..I've loved this sequence! IPBLE: Increasing Performance By Lowering Expectations. #21 20051224 11:18:52
Re: Very interesting problems..Great, Ricky, but you don't have to compute all the numbers between 1 and 100. IPBLE: Increasing Performance By Lowering Expectations. #23 20051224 11:24:12
Re: Very interesting problems..I'm still not sure what n is... At first I thought it was the size of the list (circle), but that can't be right. Could you please clarify this? "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..." #24 20051224 11:31:07
Re: Very interesting problems..I can't wait until tomorrow. n<>5 I wrote fast vb6.0 program: IPBLE: Increasing Performance By Lowering Expectations. #25 20051224 11:33:43
Re: Very interesting problems.....n<>6 IPBLE: Increasing Performance By Lowering Expectations. 