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You are not logged in. #1 20080609 10:23:18
Find a number...Find a number (mathematically & logically) which is square of the sum of its digits! Last edited by ZHero (20080609 10:26:56) If two or more thoughts intersect with each other, then there has to be a point. #2 20080609 11:04:06#3 20080609 12:07:49
Re: Find a number...
yes.. It OBVIOUSLY is the answer but how does one WORK IT OUT? Mathematically & Logically?? If two or more thoughts intersect with each other, then there has to be a point. #4 20080609 12:41:16
Re: Find a number...1 of course is the simplest nonzero answer. In order to solve for a solution, one must solve the equation: Solving this equation for a, we get: The trick now is to find b such that 36b + 100 is a perfect square. 0 works, but it leads to the trivial solution (i.e. 0) and a = 10. 1 works as well, which leads to both 81 and 1 itself. "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..." #5 20080609 12:45:13
Re: Find a number...A faster method: Last edited by JaneFairfax (20080609 12:45:59) #6 20080609 13:35:43
Re: Find a number...Jane, that method isn't based in logic, it's just an algorithmic test by exhaustion. "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..." #7 20080609 22:24:24
Re: Find a number...Proof by exhaustion is still a logical proof. #8 20080610 01:18:40
Re: Find a number...I believe you're not interpreting his words properly. The way I interpreted them is that "logical" meant that you didn't go by exhaustion, that you used logic (math) to find them instead. "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..." #9 20080610 01:24:48
Re: Find a number...Would it count as logical if you proved that no number bigger than, say, 50 could possibly fit the condition, and then tested all the others individually (treating them as special cases)? Why did the vector cross the road? It wanted to be normal. #10 20080610 02:18:32
Re: Find a number...Typically, yes. However, this does not seem to be in the same sense that ZHero is using the word. "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..." #11 20080611 07:20:54
Re: Find a number...Hi guys! If two or more thoughts intersect with each other, then there has to be a point. #12 20080611 07:51:11
Re: Find a number...Let no. be 10x+y (x,y=09;x=!0). If two or more thoughts intersect with each other, then there has to be a point. #13 20080611 08:12:35
Re: Find a number...The required number can only be 'one/two digit' number can also be shown.. If two or more thoughts intersect with each other, then there has to be a point. #14 20080611 08:33:37
Re: Find a number...
I don't agree with this. Why did the vector cross the road? It wanted to be normal. #15 20080611 09:49:44
Re: Find a number...Well, then. It looks like what ZHero means by “logically” is somewhere between my proof by exhaustion and Ricky’s algebraic proof. #16 20080611 12:06:07
Re: Find a number...Very well said mathsyperson! If two or more thoughts intersect with each other, then there has to be a point. #17 20100528 15:41:43
Re: Find a number...Consider a three digit number (100a+10b+c) ; a, b, c ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and a≠0 If two or more thoughts intersect with each other, then there has to be a point. #18 20100529 01:31:40
Re: Find a number...You need to check 2 more cases. Wrap it in bacon #19 20100529 14:47:52
Re: Find a number...
If two or more thoughts intersect with each other, then there has to be a point. 