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Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 2*97=194 so S=1+9+4=14. If n=4444 then 2*4444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.

Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 2*97=194 so S=1+9+4=14. If n=4444 then 2*4444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 2*97=194 so S=1+9+4=14. If n=4444 then 2*4444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.
Transcribed Image Text:Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such number since 9+7=16, and n=4444 is another What are the possible values for the sum of the digits, S, of 2n? Example: If n=97 then 2n= 2*97=194 so S=1+9+4=14. If n=4444 then 2*4444= 8888 and S=4*8= 32. Find all possible values for S, the sum of the digits of 2n, and prove that no other values are possible for S.
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