Guest Posted December 13, 2009 Report Share Posted December 13, 2009 N is a positive base ten integer satisfying: sod(N) + sod(sod(N)) + sod(sod(sod(N))) = 2007. where, sod(N) denotes the sum of digits of N. Determine the minimum value of N. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted December 13, 2009 Report Share Posted December 13, 2009 A 220-digit number where each digit is a 9. sod(99999.....999)=1980 sod(sod(99999.....999))=18 sod(sod(sod(99999.....999)))=9 The sum is 1980+18+9 = 2007. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted December 14, 2009 Report Share Posted December 14, 2009 A 220-digit number where the first digit is a 6 and the other 219 digits are 9s. sod(6999.....999)=1977 sod(sod(6999.....999))=24 sod(sod(sod(6999.....999)))=6 The sum is 1977+24+6 = 2007. Quote Link to comment Share on other sites More sharing options...
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Guest
N is a positive base ten integer satisfying:
sod(N) + sod(sod(N)) + sod(sod(sod(N))) = 2007.
where, sod(N) denotes the sum of digits of N.
Determine the minimum value of N.
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