```python
def identify_pronouns_and_referents(sentence):
    pronouns_referents = {}
    words = sentence.split()
    for i in range(len(words)):
        if words[i] == "they":
            referents = []
            for j in range(i-1, -1, -1):
                if words[j] in ["Alice", "Bob", "Claire", "Dave", "Eve"]:
                    referents.append(words[j])
            pronouns_referents["they"] = referents
    return pronouns_referents

def generate_sentences_with_referents(sentence, pronouns_referents):
    sentences = []
    for pronoun, referents in pronouns_referents.items():
        for referent in referents:
            new_sentence = sentence.replace(pronoun, referent)
            sentences.append(new_sentence)
    return sentences

def check_sentences(sentences):
    valid_sentences = []
    for sentence in sentences:
        if "Alice" in sentence and "Bob" in sentence and "Claire" in sentence and "Dave" in sentence and "Eve" in sentence:
            valid_sentences.append([sentence.split()[0], sentence.split()[6], sentence.split()[8], sentence.split()[12], sentence.split()[16], sentence.split()[20]])
    return valid_sentences

def determine_referents(sentence, pronouns_referents):
    generated_sentences = generate_sentences_with_referents(sentence, pronouns_referents)
    valid_sentences = check_sentences(generated_sentences)
    
    if len(valid_sentences) == 1:
        return valid_sentences[0]
    else:
        return "ambiguous"

def solve_game_problem(input_text):
    parts = input_text.split("\n")
    sentence = parts[1].split("Sentence: ")[-1]
    options = parts[-3:]
    pronouns_referents = identify_pronouns_and_referents(sentence)
    referents = determine_referents(sentence, pronouns_referents)
    
    for option in options:
        if referents[-1] in option:
            return option.split()[0]

input_text = "Alice, Bob, Claire, Dave, and Eve are dancers at a square dance. At the start of a song, they each have a partner: Alice is dancing with Jamie, Bob is dancing with Lola, Claire is dancing with Izzi, Dave is dancing with Rodrigo, and Eve is dancing with Ophelia."
options = ["(A) Jamie", "(B) Lola", "(C) Izzi", "(D) Rodrigo", "(E) Ophelia"]
final_answer = solve_game_problem(input_text)
print("Final answer: " + final_answer)
```