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Projects are independent and take 1,2 or 3 nights to complete (each equally likely). You and your spouse have dinner and each start a project

Projects are independent and take 1,2 or 3 nights to complete (each equally likely). You and your spouse have dinner and each start a project on night 1. On any night, if you and your spouse are in sync and have just finished a project, you will have dinner together. Otherwise, if just one of you finish a project, you will start a new project. What is the expected number of nights till you next dine with your spouse

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