I'm no lawyer, but from my time in the insurance business (NOT a salesman - a computer nerd), there is a contract law principle called "scrivener's error" (I'm sure someone can correct the spelling if I'm off).
It is basically a way for common sense to prevail. For example, if someone is selling you an insurance policy for $100,000, but your policy comes through for $1,000,000 with no increase in premiums, the insurance company can correct this without your consent.
This is the same principle. A hotel can't back out on a quoted rate of $100 to charge you $120. It is reasonable of you to expect a hotel room for $100.
It is unreasonable of you to expect a hotel room for free. Therefore they can back out of this.
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"I will not be pushed, filed, stamped, indexed, briefed, debriefed or numbered. My life is my own."