Smith quarreled; they struck each other" is correct. "Jones, Smith and
Brown quarreled; they struck one another" is also correct. Don't say,
"The two boys teach one another" nor "The three girls love each other."


EACH, EVERY, EITHER, NEITHER

These words are continually misapplied. _Each_ can be applied to two
or any higher number of objects to signify _every one_ of the number
_independently_. Every requires _more than two_ to be spoken of and
denotes all the _persons_ or _things_ taken _separately_. _Either_
denotes _one or the other of two_, and should not be used to include
both. _Neither_ is the negative of either, denoting not the other,
and not the one, and relating to _two persons_ or _things_ considered
separately.

The following examples illustrate the correct usage of these words:

_Each_ man of the crew received a reward.

_Every_ man in the regiment displayed bravery.

We can walk on _either_ side of the street.

_Neither_ of the two is to blame.


NEITHER-NOR

When two singular subjects are connected by _neither_, _nor_ use a