You receive an offer in the mail that says you're eligible to win a cash prize if you place some stickers on a form and return it to the sender. What type of contract is this?

unilateral contract

Explanation:

Based on the information provided within the question it can be said that in this scenario the type of contract being used is called a unilateral contract. This is a contract in which the "offerer" makes a promise in exchange for the receiver performing a certain action. Which in this case the promise is that they enter for a chance to win a cash prize if they place a sticker and send the form (which is the performance.)