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Self-Referential Numbers (Posted on 2005-09-23) Difficulty: 3 of 5
A nine digit number has the property where the first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, the third digit equals the number of twos and threes used in the number, etc. through the ninth digit equals the number of eights and nines used in the number. What could the number be?

A ten digit number has a similar property to the nine digit number. The first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, etc. through the ninth digit. And also, the tenth digit equals the number of zeros and nines used in the number. What could this number be?

See The Solution Submitted by Brian Smith    
Rating: 3.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Attn: Ken Haley | Comment 9 of 19 |
(In reply to Attn: Ken Haley by Penny)

re: "My program (updated in the original post) now runs in 12 seconds on my desktop. Yours is running in 25 seconds. (Not sure why mine is now running about twice as fast as yours.)"

Your program runs on my desktop in 13 seconds when your last "For" is changed to strict equality:

For i10 = Min(9, 20 - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8 - i9) _
To Min(9, 20 - i1 - i2 - i3 - i4 - i5 - i6 - i7 - i8 - i9)

  Posted by Penny on 2005-09-24 12:20:58
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