At the track one day, Bill speaks to Arnold, offering to buy Arnold's prize harness racer, Smokey, for $50,000. Arnold replies that he will sell for $60,000. Bill refuses. Two days later Bill deposits an envelope in the mailbox addressed to Arnold containing a cheque for $60,000 and including a note saying that he accepts Arnold's offer to sell Smokey. The next day, Arnold receives a letter from Sam which says that Sam will buy Smokey for $70,000 and if he hears nothing further from Arnold within twenty-four hours he will consider that Arnold has sold Smokey to him for that price. On receiving Sam's letter Arnold intends to sell Smokey to Sam for $70,000 but two days later Tom offers him $80,000 for the horse. Arnold then mails a letter to Tom accepting his offer. Later that day, Arnold receives Bill's envelope. The next day Tom telephones Arnold to say that he wishes to withdraw his offer to buy Smokey. A day later, Tom receives Arnold's letter accepting Tom's offer.

Has Arnold made a contract with Bill? Has Arnold made a contract with Sam? Has Arnold made a contract with Tom? Explain your answer, referring to the relevant legal principles.