Do the tug of war rules have a typo? ("Or" vs. "nor")

Solution 1:

Nor is generally only used in conjunction with neither, so you could rewrite the sentence as:

The rope must be neither less than 10 centimetres (100 mm), nor more than 12.5 centimetres (125 mm) in circumference...

... but that's not necessary. The sentence is just fine as it stands.

You're parsing the sentence as if "not" and "or" were in opposition. They're not: "less" and "more" are the alternatives here. It might make more sense if you strip it down to:

...must not be less or more

Solution 2:

Although there are some people who are afraid to use nor without neither, that seems silly to me. I would certainly have written nor there in your example sentence. The OED supports this very sort of thing in its sense 3a for nor conj.¹ (and adv.), which is:

3a. Following a word or phrase which is negated with not, never, etc.

Here are two of its citations for that sense:

• 1934 ‘M. J. Farrell’ Devoted Ladies i. 36
  One must not be harsh to him, nor must an author betray too great a knowledge.
• 2002 K. Matinuddin Nuclearization of S. Asia x. 200
  Non-Nuclear Weapon States..who are party to the Treaty, undertake not to receive nuclear weapons nor to manufacture them.

See? Perfectly natural. Your sentence involves an instance following not, which is directly covered above. I would have used nor.

There are other senses of nor without a corresponding neither, but I shall not list those here.

Nor shall I list them down here.

Nor here, either. :)