Gently drop the egg into the bowl of water. If it:
sinks to the bottom and stays there, it is about three to six days old.
Sinks, but floats at an angle, it's more than a week old.
Sinks, but then stands on end, it's about two weeks old.
Floats, it's too old and should be discarded.
For a test just to see if the eggs are all right to use, dissolve 2 tablespoons salt in 2 cups cold water, then put the egg in the water. If it sinks, it's good; if it floats, it's too old.
Eggs act this way in water because of the air sac present in all eggs. As the egg ages, the air sac gets larger because the egg shell is a semi-permeable membrane. The air sac, when large enough, makes the egg float. Eggs are generally good for about three weeks after you buy them.
And how do you see if an egg is hard cooked? Spin it on a flat surface. If the egg wobbles, it's fresh because the insides are moving around. If the egg spins smoothly, it's cooked.