Final answer:
Whether Martin can sue Claire for breach of contract depends on the specific terms of the contract and the application of legal doctrines like impossibility or frustration of purpose.
Step-by-step explanation:
In the scenario where Claire signs a contract with Martin to play the piano at his birthday party but injures her hand prior to the performance, making her unable to fulfill the contract, the question of whether Martin can successfully sue Claire for breach of contract is complex.
Generally, if a party to a contract is unable to perform due to unforeseen circumstances beyond their control, such as an accidental injury, this may constitute an excusable nonperformance under legal doctrines like impossibility or frustration of purpose. Therefore, it may not be accurate to say that Martin can sue Claire for breach of contract due to nonperformance without considering the specific circumstances and terms of the contract.