Final answer:
The claim that suitors must string Odysseus's mandolin to win Penelope is false; instead, they must string his great bow and shoot an arrow through twelve axe heads, per 'The Odyssey'.
Step-by-step explanation:
The statement that the suitors must string Odysseus's mandolin to win Penelope's hand in marriage is false. In Homer's epic, 'The Odyssey', the suitors are required to string Odysseus's great bow and shoot an arrow through twelve axe heads. This challenge, known as the Test of the Bow, was designed so that only Odysseus could complete it and reveal himself to the suitors and reclaim his wife and kingdom.