Consider an infinite sequence a1,a2,⋯ whose terms all belong to {1,2}. A positive integer with n digits is said to be good if its decimal representation has the form arar+1⋯ar+(n−1), for some positive integer r. Suppose that there are at least 2008 good numbers with a million digits. Prove that there are at least 2008 good numbers with 2007 digits. linear algebramatrixinductioncombinatorics proposedcombinatorics