The contract would be ambiguous on its face. Therefore, the Court will accepte whatever "extrinsic evidence" (i.e. evidence beyond the language of the contract) the parties offered at an evidentiary hearing, to determine what was intended.
If the Court was able to determine what was intended, the contract would be enforced consistent with the intent of the parties.
If Court determined that there was not a "meeting of the minds" and that the parties never shared the same intent, then the Court would rule that no contract had been formed.
If some work had been performed despite the lack of a valid contract formation, then the person who did the work would be entitled to compensation in an amount equal to the fair market value of the work actually done, under a legal theory sometimes called "quantum meruit" and sometimes called "unjust enrichment" or "restitution."