"Surtido" Numbers
Source: Mexican Mathemathical Olympiad, 2006
November 25, 2007
number theory proposednumber theory
Problem Statement
Let n be the sum of the digits in a natural number A. The number A it's said to be "surtido" if every number 1,2,3,4....,n can be expressed as a sum of digits in A.
a)Prove that, if 1,2,3,4,5,6,7,8 are sums of digits in A, then A is "Surtido"
b)If 1,2,3,4,5,6,7 are sums of digits in A, does it follow that A is "Surtido"?