What physical feat was used in the "olden days" to determine if a child was old enough to attend school?

This is probably a myth but maybe it was to reach his arm over his head and touch his ear. Children under five (more or less) can't do this because their arms are too short in preportion to their heads.

If you have a four year old in the family it is great fun to tell them to try this. (As long as you don't tease them they'll think it's funny.)

I remember reading this in a paper when my little sister was three. I asked her to try and we laughed and laughed when she couldn't but I could. A year and a half later we were goofing around and she scratched her back and suddenly got a bright look on her face. "Hey, I can do it now!" and demonstrated. I was amazed she remembered.

A few weeks after I read it in the paper there was a "Prince Valiant" comic strip that mentioned it was a test in Camelot to determine if a boy was old enough to start training as a squire.

I think that in order to find out, the child's head would be of normal size (when a baby is first born, it has a large head). They possibly would also check the height, and then they would admit them. I'm not so sure, however.

Generally 5yrs old but it depended on the accessibility of a school or if the parents had the ability to home school

Tie shoelaces?

Probably their mouths, if they could talk they could be taught.