BMAD Posted November 17, 2014 Report Share Posted November 17, 2014 Given 1962 -digit number that is divisible by 9. Let x be the sum of its digits. Let the sum of the digits of x be y. Let the sum of the digits of y be z. Find z. Quote Link to comment Share on other sites More sharing options...
0 DejMar Posted November 18, 2014 Report Share Posted November 18, 2014 (edited) The digital root of any number divisible by 9 (other than 0), is 9. Let a repdigit number be denoted as x(y), such that y is the number of digits and x is the repeated digit. From 1 ≤ n < 9(11), the digital sum of a number divisible by 9 is < 99. The digital sum of that number is 9. From 9(11) ≤ n < 9(1(11)), the digital sum of the digital sum of a number divisible by 9 is < 99. The digital sum of the resulting number is 9. A 1962-digit number is < 9(1(11)), therefore, given n is the 1962-digit number and S(k) is the digit sum function of k, z = S(S(S(n))) = 9. Edited November 18, 2014 by DejMar Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 9, 2014 Report Share Posted December 9, 2014 Suppose the number were all 9's.x would be 17,658, y would be 27, making z=9. Quote Link to comment Share on other sites More sharing options...
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BMAD
Given 1962 -digit number that is divisible by 9. Let x be the sum of its digits. Let the sum of the digits of x be y. Let the sum of the digits of y be z.
Find z.
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