Because each row must have every element of the group represented exactly once, it is easy to see that the two blank spots in the "b" row must be occupied by "d" or "f". However, if one examines the columns containing these two blank spotsthe "d" and "f" columnsone finds that "d" and "f" have already been filled in on both, which means that regardless of how "d" and "f" are placed in row "b", they will always violate the permutation rule. Because our algebraic deductions up until this point were sound, we can only conclude that our earlier, baseless assumption that "ab" = "c" was, in fact, false. Essentially, we guessed and we guessed incorrectly. We, have, however, learned something: "ab" ≠ "c".