When should I use each other and when should I use one another?
This is an interesting usage note extracted from the "each other" page of Yahoo! Education (emphasis added). It answers your question.
It is often maintained that each other should be used to denote a reciprocal relation between two entities, with one another reserved for more than two: thus The twins dislike each other but The triplets dislike one another.
Sixty-four percent of Usage Panelists say that they follow this rule in their own writing. But it should be pointed out that many reputable writers from Samuel Johnson onward have ignored the rule and that the use of each other for more than two, or of one another for two, cannot be considered incorrect.
In particular, there are contexts in which each other and one another are subtly different in meaning. When speaking of an ordered series of events or stages, one another is the preferred form. Thus the sentence The waiters followed one another into the room was preferred by 73 percent of the Usage Panel to the sentence The waiters followed each other into the room.
Each other refers to two, one another to more than two. "Jones and 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."
- Use “each other” when referring to two things.
- Study the use of “each other” in these instances: "The two dogs looked at each other. The boy and the girl help each other."
- Use “one another” when referring to three or more things.
- Note the use of “one another” in this instance: The dog, cat and bird looked at one another.
- Remember one small exception to the rule, as pointed out by the Associated Press Stylebook. When referring to an indefinite number, either “each other” or “one another” can be used. For example: We love each other. We love one another
Some handbooks and textbooks recommend that each other be restricted to reference to two and one another to reference to three or more. The distinction, while neat, is not observed in actual usage. Each other and one another are used interchangeably by good writers and have been since at least the 16th century.
Source: Merriam-Webster Dictionary