"They wrote each other every week."

[stramner]

Doesn't "every other" mean "every second"? I wrote "psali si každej druhej týden" and it was wrong

[VladaFu]

It is "each other" and "every week", the "other" belongs to "each" not to "every". What you suggest would be "They wrote each other every other week."

Also, "každej druhej" is Common Czech, are you sure it is supposed to be accepted? If yes, then "tejden" is in order to stay consistent. But in written form it looks like 18th century, it is normally only spoken.