Problem on a business law exam...?

so i had this question on my business law exam and was unsure of the answer....

Party A offers to sell a piano to party B for 500$. Party B tells party A that he wants 2 weeks to think the offer over...Party A gives Party B two weeks and writes it down on paper. Party B, in the middle of the 2 weeks tells party A that he wants the piano for 450$...Party A does not respond...Party B goes to Party C's house one day and sees a piano..Party B inquires on the piano and finds out that party C bought the from Party A for 600$. Party B admires the beauty of the piano and tells Party A that he wants the piano for 500$...A refuses to sell the piano as A has already sold it....B sues A for breach of contract who wins in this situation?

this is based off NY LAW

When B told A he wanted the piano for $450, that was a counteroffer, which includes a rejection of the original offer to sell at $500. This canceled A's obligation to hold the offer open. A wins.

** The writing makes no difference. The important fact is that B's lower offer is a "counter offer", and a counter offer contains a Rejection. B released A from holding it open, by basically saying "I don't want it at 500."

Had he said "WOULD YOU TAKE 450?" that would not have been a counter offer, but an Inquiry. Had A said "No, the Price is 500" that would have renewed the offer and he probably would be stuck with the full two weeks.

A wins. Unless he hires a schmuck for a lawyer.

id say that party B didnt hold up to his end of the cantract of paying the 500 and says so by saying he wants it for 450. So party A can sell it to whoeveras party B refused to pay 500. But is it a personal sale? or is party A in a buisness?

"Wrote it on paper".... WHAT did they write on the paper and did both parties sign it?