Chapter $10$: Contract Formation Rocky Mountain Case $-$ Availability Ends

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Rocky Mountain Races sponsors the Pioneer Trail Marathon with an advertised first prize of $$10,000.$ The rules require the competitors to run $100$ miles from the floor of Blackwater Canyon to the top of Pine Mountain. The rules also provide that Rocky reserves the right to change the terms of the race at any time. Monica enters the race and is declared the winner. Rocky offers her a prize of $$1,000$ instead of $$10,000.$

Did Rocky and Monica have a contract?

If so$,$ was it a bilateral or unilateral contract? How would such a contract be accepted?

If so$,$ is Rocky required to give a prize of $$1,000$ or $$10,000?$