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        riddles >> easy >> 10 digit number
        
(Message started by: BNC on Feb 5^th, 2003, 10:35am)

Title: 10 digit number
Post by BNC on Feb 5^th, 2003, 10:35am

Find a 10-digit number, such that the leftmost digit equals the number of "1"s in the number, the 2nd equals the number of "2"s, and so on until the 9th digit that equals the number of "9"s and the 10th that equals the number of "0"s.

Title: Re: 10 digit number
Post by poseur on Feb 5^th, 2003, 1:38pm

[hide]that's the same puzzle as the one that said, "This sentence the digit 1 ___times." but with every number decreased by one and shifted one spot over. [/hide]

Title: Re: 10 digit number
Post by Icarus on Feb 5^th, 2003, 7:41pm

on 02/05/03 at 13:38:18, poseur wrote:

[hide]that's the same puzzle as the one that said, "This sentence the digit 1 ___times." but with every number decreased by one and shifted one spot over. [/hide]

While the puzzles are similar they are not the same. The solution I found for this puzzle does not work for the other puzzle (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1044188498) and neither do the solutions posted for that one work here.

I have found 1 solution so far. BNC, do you know if there are more?

Title: Re: 10 digit number
Post by aero_guy on Feb 5^th, 2003, 9:24pm

OK, I got one solution, but calling it a ten digit number is a little misleading.

[hide] 0000000009 [/hide]

I didn't read the referenced thread, is this along the same lines?

Title: Re: 10 digit number
Post by BNC on Feb 5^th, 2003, 11:06pm

It is a "real" ten-digit number (leftmost digit is not 0), and it can be proved to have a single solution.

And yes, it is similar in construction to the other puzzle, but very different in solution (e.g., a unique solution).

I like this one better!

Title: Re: 10 digit number
Post by Pietro K.C. on Feb 6^th, 2003, 8:58am

Aero_guy, you might want to recheck that answer... :)

The one I got was 2100010006, and BNC claims uniqueness...

I did it as follows:

Start with 0000000000
correct # of 0's: 0000000009
correct # of 9's: 0000000019
correct # of 0's: 0000000018
correct # of 9's and 8's: 0000000108
correct # of 1's: 1000000108
correct # of 1's and 2's: 2100000108
correct # of 0's and 6's: 2100010006
Ta-da!

Title: Re: 10 digit number
Post by BNC on Feb 6^th, 2003, 9:08am

Anyone cares to take a stab at showing uniqueness?

:D

Title: Re: 10 digit number
Post by poseur on Feb 6^th, 2003, 10:04am

The numbers may be different, but follow exactly the same pattern.
The other puzzle had the answer, 1732111211.
Shift the first digit to the end because this puzzle ends with zero:732111211.
Subtract one because you don't have the extra digits in the sentence itself: 6210001000.
And move everything over one place because each number now refers to a different digit (eg 6 0's instead of 6 1's) and you get:2100010006.
Same puzzle.

Title: Re: 10 digit number
Post by BNC on Feb 7^th, 2003, 3:23am

on 02/06/03 at 10:04:15, poseur wrote:

<snip>
Same puzzle.

Oops. Yes. Sorry... :-[

Title: Re: 10 digit number
Post by BNC on Feb 12^th, 2003, 1:24am

A hint for showing uniqueness (it not hard, I just thought to *BUMP* the thread):

[hide]
The key is round.... you can count on it
[/hide]