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        riddles >> easy >> Math riddle?
        
(Message started by: x2862 on Jul 19th, 2009, 1:02pm)
Title: Math riddle?
Post by x2862 on Jul 19th, 2009, 1:02pm
Can you rearrange the digits of a number n to obtain 2n? Note: n must be a whole number in base 10. I've been trying to find a solution for a long while and found nothing. any help would be nice.
Title: Re: Math riddle?
Post by towr on Jul 19th, 2009, 2:09pm

on 07/19/09 at 13:02:22, x2862 wrote:
Can you rearrange the digits of a number n to obtain 2n? Note: n must be a whole number in base 10. I've been trying to find a solution for a long while and found nothing. any help would be nice.
Yes, you can.
[hide]Consider the decimal expansion of 1/7[/hide]
Title: Re: Math riddle?
Post by pex on Jul 19th, 2009, 3:18pm
Interestingly, there are [hide]twelve[/hide] possible values for n less than a million, and they all use the same set of digits!
Title: Re: Math riddle?
Post by R on Sep 14th, 2009, 12:26am

on 07/19/09 at 14:09:50, towr wrote:
Yes, you can.
[hide]Consider the decimal expansion of 1/7[/hide]

How did you find this?

@Pex
You too!!!
Title: Re: Math riddle?
Post by pex on Sep 14th, 2009, 12:40am

on 09/14/09 at 00:26:15, R wrote:
How did you find this?

@Pex
You too!!!

As for me, I simply wrote a bit of code to try all numbers less than a million. towr's solution relies on a well-known property of decimal expansions of fractions:
[hide]1/7 = 0.142857142857...
2/7 = 0.285714285714...
3/7 = 0.428571428571...
4/7 = 0.571428571428...
5/7 = 0.714285714285...
6/7 = 0.857142857142...[/hide]
Title: Re: Math riddle?
Post by towr on Sep 14th, 2009, 12:55am

on 09/14/09 at 00:26:15, R wrote:
How did you find this?
I remembered it from when it came up in a similar question.
Title: Re: Math riddle?
Post by R on Sep 14th, 2009, 5:35am

on 09/14/09 at 00:40:14, pex wrote:
As for me, I simply wrote a bit of code to try all numbers less than a million.

Ah! Disappointing!!!


Quote:
towr's solution relies on a well-known property of decimal expansions of fractions:
[hide]1/7 = 0.142857142857...
2/7 = 0.285714285714...
3/7 = 0.428571428571...
4/7 = 0.571428571428...
5/7 = 0.714285714285...
6/7 = 0.857142857142...[/hide]

Can you elaborate on  that property or give link to some good source?


on 09/14/09 at 00:55:49, towr wrote:
I remembered it from when it came up in a similar question.

Well I was going to add "Or you knew this?" and just didn't. I thought, YOU must be having good logical approach anyway.
Title: Re: Math riddle?
Post by towr on Sep 14th, 2009, 6:29am

on 09/14/09 at 05:35:04, R wrote:
Well I was going to add "Or you knew this?" and just didn't. I thought, YOU must be having good logical approach anyway.
Nah, if I hadn't remember this, I'd have used pex's approach and run a program.
Title: Re: Math riddle?
Post by pex on Sep 14th, 2009, 9:08am

on 09/14/09 at 05:35:04, R wrote:
Can you elaborate on  that property or give link to some good source?

MathWorld (http://mathworld.wolfram.com/CyclicNumber.html) has a page on it.
Title: Re: Math riddle?
Post by victorpride on Feb 10th, 2010, 8:27pm
umm the question specifically stated it must be a whole number.
Title: Re: Math riddle?
Post by ThudanBlunder on Feb 10th, 2010, 9:47pm

on 02/10/10 at 20:27:48, victorpride wrote:
umm the question specifically stated it must be a whole number.

[hide]142857 x 2 = 285714[/hide]


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