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ALGEBRAIC PROCEDURE FOR COUNTING DIGITS Edson E S Sampaio∗ November 17, 2012 Definition of problems Let a be a digit from 1 to 9, N and q be positive integers and the algebraic expression, Q(N|a) = q, mean: the amount of digits a used to write all integers from 1 to N equals q. First problem: Determine q from the values of a and N. Second problem: For every a, determine the minimum value of N such that q = N, except for the trivial solution Q(1|1) = 1. A variation of this second problem involves

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