punctuation - Preposition ambiguity and comma placement

1: They were running and jumping and playing in the field.

2: They were running, jumping, and playing in the field.

3: They were running and jumping, and playing in the field.

In which of these sentences does "in the field" refer to (modify?)...
A: All three verbs (running, jumping, playing)
B: Only playing
C: Either all three, or only playing. It's ambiguous.

Also, I assume all three sentences are acceptable in terms of punctuation, tell me if they are not.
And I'm sure you can rearrange the sentence or add/change words to make the meaning more clear, but for my sake, don't. Thanks in advance.

Answer

CORRECT ANSWER: A: All three verbs (running, jumping, playing)

1: They were running and jumping and playing in the field.

2: They were running, jumping, and playing in the field.

3: They were running and jumping, and playing in the field.

Let's diagram:

They / were running / were jumping / were playing / in the field

Subject: They

Verb: [Compound Verb (all three verbs were running, were jumping, were playing share the same subject)] e.g. They were running. They were jumping. They were playing.

Adverb prepositional phrase modifies the Compound Verb to describe "Where?" "Where were they running, jumping, and playing?" In the field.

The phrase modifies all three verbs. The verbs are part of a verb phrase that has a helping verb (a.k.a. auxiliary verb) were + a main verb running, jumping, playing The "were" may be omitted but understood and STILL the helping verb in the verb phrase:

Illustrated:

1: They were running and (were) jumping and (were) playing in the field.

2: They were running, (were) jumping, and (were) playing in the field.

3: They were running and (were) jumping, and (were) playing in the field.

Number 3 is grammatically incorrect since all three verbs in the same verb phrase share the same subject. Number 2 is the proper way to write it.

"2f. Two or more verbs joined by a connecting word and having the same subject are called a compound verb."--John E. Warriner. Warriner’s English Grammar and Composition. Fourth Course. Franklin Edition. Orlando, Florida: Harcourt, Brace, and Jovanovich. 1982. 35.

Two examples given in the book:

On our last trip to Europe, we sailed on a freighter and saved a great deal of money. [compound verb: sailed (and) saved; subject: we]

I have cut the grass and clipped the hedges. [The subject is I; the compound verb is have cut (and) have clipped. Notice that the helping verb have goes with cut and clipped.]