Problem

Source: Romanian JBTST VI 2007, problem 4

Tags: number theory proposed, number theory



We call a real number $x$ with $0 < x < 1$ interesting if $x$ is irrational and if in its decimal writing the first four decimals are equal. Determine the least positive integer $n$ with the property that every real number $t$ with $0 < t < 1$ can be written as the sum of $n$ pairwise distinct interesting numbers.