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You are not logged in. #1 20060312 05:23:00
A Powerful PuzzleI like this one That's x raised to the power of x raised to the power of x, going on forever equals 2. Solve for x. Last edited by fgarb (20060312 05:23:41) #3 20060312 07:04:27
Re: A Powerful PuzzleIt still hurts my brain, and I know the answer! Incidentally, if anyone can solve this, then I have a followup. Don't try them in the reverse order though, if you do it has the potential to be seriously confusing! #5 20060312 12:44:08
Re: A Powerful PuzzleIf I am right about the first one, I reckon that solving for 10 would only give a very slightly higher answer, but I don't have the time right now! #6 20060312 13:15:29
Re: A Powerful PuzzleWell, not entirely, but it is right if you've roundeded it. But the real question is... what is 1.414 more commonly expressed as? Why did the vector cross the road? It wanted to be normal. #7 20060312 15:58:59
Re: A Powerful PuzzleLet Therefore, ***someone continue from where I have left...*** Character is who you are when no one is looking. #8 20060312 16:37:12
Re: A Powerful PuzzleThat is definitely correct, and it should be straightforward from where Ganesh left it. Now, it should be pointed out, as mathsyperson said, that the solution you get for y=10 in this way is lower than for y=2. has a solution. Unfortunately, I think you'll need to know calculus to be able to figure this out, but the answer makes me wonder if there's something really deep going on here that I don't understand. I find this really interesting! Last edited by fgarb (20060312 16:38:16) #9 20060312 17:07:20
Re: A Powerful PuzzleI think I can declare that there is no solution for the above equation. The highest value of y for is y=e or 2.7182818284 approximately and the highest value of x for finite y is x=1.444667861 approximately. I am sure it can be proved that has no solution. Character is who you are when no one is looking. #10 20060312 17:21:19
Re: A Powerful PuzzleThat is what I get as well. If anyone has any idea why e ends up a solution to this problem, I'd love to hear it! That annoying constant seems to have a way of popping up everywhere. #11 20060312 21:06:05
Re: A Powerful Puzzle
Mathsy, yes, I did round it and I do I know what it is expressed as  just wanted to leave something in the puzzle for someone else! #12 20060312 22:47:21
Re: A Powerful PuzzleAh. Fair enough. Sorry. Why did the vector cross the road? It wanted to be normal. #13 20060330 05:52:55
Re: A Powerful PuzzleWell to phrase the problem in some other way.... Last edited by sabujakash (20060330 05:56:08) #14 20060330 07:56:38
Re: A Powerful PuzzleYes sabujakash, above the magic number 1.44466786... the series diverges. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman 