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There is a legally binding contract between A and B.
B's letter to A was an offer and A accepted it by post. On the same day, B posted his letter of revocation.
An offer can be revoked anytime before, but not after, acceptance. So we need to consider which event took place first.
In general, acceptance is not valid until it is acctually communicated. An exception to this is acceptance by post, which took place at the time the letter is posted (Adams v. Lindsell). Hence, A's acceptance took place at 2:00 on 23 Dec, which was before B's specified deadline.
The postal rule exception does not apply for revocation of offer. Revocation by post does not take place until it is delivered (Stevenson v. McLean). Therefore, B's revocation did not take effect until it was received by A, i.e. until 8:00 on 25 Dec.
Hence, B's recovation took place after A's acceptance and was invalid. A binding contract was formed between A and B at 2:00 on 23 Dec, the time when A posted his letter of acceptance.