In answer to the question,

What is the significance of the solution to the "Riddle of the Sphinx"?

The riddle, or course, was this: What is it that goes on four legs in the morning,two legs at evening and three at night? To which Oedipus answered correctly, Man,who crawls as a baby on four legs in the morning,or beginning of his life,walks on two legs most of his life,but needs the assistance of a walking stick,or third leg,as he approaches old age. When Oedipus solved it he was rewarded with kingship and a wife (his mother). The myth-writers would have us believe that if these aren't signs of success, what are? To answer correctly yielded life, and incorrectly meant the pain of death. Yet, did Oedipus truly solve the riddle? Since he was responsible for causing the plague of the Sphinx (by unwittingly killing his father Laius), when he answers the riddle the plague ceases. Should we really be happy? He starts the trouble and he stops it. A sum of zero, if you ask me.

The deeper story in Oedipus, then, seems to betray a more cynical outlook: I have to wonder if the answer, Man, isn't but another riddle. Let's face it: the Greeks are renowned for having sifted reason from mythology and history. Where the religions of the Levant emphasize dependence on God, the Greeks chose to emphasize dependence on man, a truly humanistic philosophy. In other words, they conceived of life as a riddle/mystery with man at the center/solution. One could extend this a little by arguing that the answer, Man is a metaphor for Life: the better answer to the riddle of what walks on four legs in the morning, two in the afternoon and three in the evening is Life itself! From birth to maturity through to old age. This is also in keeping with the philosophy of the Greeks.

Since Oedipus is the one responsible for starting the plague of the Sphinx, it is in a sense his riddle the Sphinx is asking, his answer which solves it and his fate that proves the mystery of life. How is "Man" an answer? Man is a mystery if there ever was one. Moreover, how is it that we have come to celebrate Oedipus solving the Riddle of the Sphinx? Oedipus is a tragic character, and if we learn anything from him it is that you cannot change your fate. The only solution here is another riddle!