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Topic: 10 digit number (Read 1813 times) |
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BNC
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10 digit number
« on: Feb 5th, 2003, 10:35am » |
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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.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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poseur
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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.
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Icarus
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Re: 10 digit number
« Reply #2 on: Feb 5th, 2003, 7:41pm » |
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on Feb 5th, 2003, 1:38pm, poseur wrote:| 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. |
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While the puzzles are similar they are not the same. The solution I found for this puzzle does not work for the other puzzle 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?
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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aero_guy
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Re: 10 digit number
« Reply #3 on: Feb 5th, 2003, 9:24pm » |
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OK, I got one solution, but calling it a ten digit number is a little misleading.
0000000009
I didn't read the referenced thread, is this along the same lines?
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BNC
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Re: 10 digit number
« Reply #4 on: Feb 5th, 2003, 11:06pm » |
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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!
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Pietro K.C.
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Re: 10 digit number
« Reply #5 on: Feb 6th, 2003, 8:58am » |
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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!
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| « Last Edit: Feb 6th, 2003, 8:58am by Pietro K.C. » |
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BNC
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Re: 10 digit number
« Reply #6 on: Feb 6th, 2003, 9:08am » |
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Anyone cares to take a stab at showing uniqueness?
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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poseur
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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.
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BNC
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Re: 10 digit number
« Reply #8 on: Feb 7th, 2003, 3:23am » |
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on Feb 6th, 2003, 10:04am, poseur wrote:
Oops. Yes. Sorry... 
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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BNC
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Re: 10 digit number
« Reply #9 on: Feb 12th, 2003, 1:24am » |
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A hint for showing uniqueness (it not hard, I just thought to *BUMP* the thread):
The key is round.... you can count on it
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| « Last Edit: Feb 12th, 2003, 1:25am by BNC » |
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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