Is "settle it through a race" correct?

Question

For this question

Let's settle it _________ race.

Can we say let's settle it through a race? Is is it correct?

Answer 1

It sounds more natural to this US English speaker to say that we settle it with a race. For example,

When it's a grudge match, when there's bad blood, wouldn't I rather settle it with a few rounds of old-fashioned boxing...

"Settle it by _____" is also possible:

If any dispute arises out of this agreement the parties will attempt to settle it by negotiation.

...the entity must or can settle it by delivering shares.

but when using by we normally use a mass noun or a gerund, like "by ___ing" or "by means of" or "by negotiation"; using by with a count noun seems to be unusual, although I can't explain an exact reason why that is so.

So either "settle it with a race" or "settle it by racing" would sound fairly normal.