The Riddle of the Sphinx originated in Ancient Egypt and carried over into Ancient Greek culture by way of Greek scholars studying at the Library of Alexandria. I believe the original author of the Egyptian version was someone interested in astronomy. The answer is "The Sun", not "man". It can be physically demonstrated with two sticks placed in the ground during the setting of the sun. I have included a link to the solution I wrote a few years back explaining exactly how to do this and explains the reasoning behind what I believe to be the solution. Something kids interested in science will enjoy.
First know that a man by the name of Eratosthenes used a stick to determine the circumference of the earth. One thing that led him to that conclusion is that at noon, in a place he called Syene, the sun would cast no shadow, as it was directly over or above. So, what does Eratosthenes, a stick, the sun, and shadow have to do with the solution? To see the solution, you simply have to go into an open field at sunset with two straight sticks.
Take one stick and place it in the ground; it will cast a shadow.
Take the second stick and place inside the shadow of the first stick.
Leave your sticks for the night and come back in the morning. What would you see? Because we live on a giant globe that is tilted at 23.4 degrees you would see the effect of the sun casting the shadow at a different angle, and you would also see the solution to The Riddle of the Sphinx.
So how can the sun be said to walk on four feet in the morning, two at noon, and three in the evening? You “mute” its “voice” by using shadow. In the morning, the two sticks are casting two shadows, and we can think of them as four legs. At noon, mayber not in your particuliar part of the world, but certainly in Syene, the sticks would cast no shadow, because the sun is directly over the sticks.
In the evening when the sun sets the two shadows will merge into one shadow again, giving the appearance of two sticks with one long shadow, and therefor only three legs.