Due South in the Northern hemisphere, due North in the Southern hemisphere.
Which Direction Does Shadow Point At Noon?
This question is relative to the position on the globe of the object casting the shadow. At noon on the equator there should be little to no shadow at all except what is directly underneath the object and it will not point any direction. If you are in parts of Alaska or Canada for about half a year you cannot even cast a shadow as the Sun will not be present to give the needed light.
Suffice it to say that if the object can cast a shadow in a particular direction as opposed to directly underneath the object, the shadow will point in the opposite direction of the Sun. If you are north of the equator it places the light rays emerging from south of you. My guess would be the shadow would point in a northern direction and likewise for if you are south. I cannot think of a situation where a shadow would point either east or west in this situation.
Suffice it to say that if the object can cast a shadow in a particular direction as opposed to directly underneath the object, the shadow will point in the opposite direction of the Sun. If you are north of the equator it places the light rays emerging from south of you. My guess would be the shadow would point in a northern direction and likewise for if you are south. I cannot think of a situation where a shadow would point either east or west in this situation.
You don't have a shadow at noon.
If you are on the equator, there is no shadow.