Final answer:
The correct answer is b) You should not have to pay; promissory estoppel applies. A lack of consideration and failure to send a timely letter of acceptance are additional factors supporting this answer.
Step-by-step explanation:
The correct answer is b) You should not have to pay; promissory estoppel applies. Promissory estoppel is a legal doctrine that allows a party to enforce a promise even if there is no valid contract. In this case, the professor can argue that she relied on your promise of sending her a check for $100,000 and took no action to change her position. Therefore, you may be prevented from going back on your promise.
Additionally, there is a lack of consideration for a valid contract. Consideration is a legal requirement for a contract, and it refers to something of value exchanged by the parties. In this scenario, the professor did not provide anything of value in return for your promise, so there is no consideration and no valid contract.
Insanity is not a valid defense in this case, as there is no indication that you were insane or unable to understand the consequences of your actions. The professor's failure to send a timely letter of acceptance is also irrelevant as you made the promise without requiring acceptance in writing.