According to Nolo.com five requirements must be met for an agreement to be binding and enforceable by a court.
Your scenario meets one requirement at best (see comments). Therefore, there is no legally binding agreement.
To be enforceable by a court, every contract (whether written or oral)
must meet several requirements. Let's take a look at each of them.
Consideration. As Cole Porter wrote in the song, True Love, "You give to me and I give to you." That sums up consideration. Each party
has to promise or provide something of value to the other. Without
this exchange, there is no contract. (Learn more in Nolo's article
Consideration: Every Contract Needs It.)
Offer and acceptance. There must be a clear or definite offer to contract ("Do you want to buy this?") and an unqualified acceptance
Legal purpose. The purpose of the agreement must not violate the law. For example, you won't be able to enforce a loan agreement that
charges interest in excess of what is allowed by usury laws or a
service agreement to hire someone to rob a bank or kill your
Capable parties. To be "capable" of making a contract, the parties must understand what they're doing. For example, there is a
presumption that minors and insane people usually don't know what
they're doing and, for that reason, contracts they enter into won't be
enforced under certain circumstances. (Learn more in Nolo's article
Who Lacks the Capacity to Contract?)
Mutual assent. This is also sometimes referred to as a "meeting of the minds." The contracting parties must intend to be bound by their
agreement and must agree on the essential terms.
If this isn't enough, there is another common law defense available to such a defendant called estoppel. Courts look to the behavior of the parties to determine if there was an actual contract or not. If the behavior does not fit the alleged agreement, then the plaintiff is estopped from enforcing the words on paper.