It's always happy at the banana stand

Sandip, Tracy, Jamal, and Sheng are best friends who work together everyday at a banana stand. Since they are so close, their happiness on any given day depends on the happiness of the other three people on the previous day. Suppose they behave as follows:

  • Sheng is happy today only if Tracy and Jamal were both happy yesterday.
  • Jamal is happy today only if Sandip or Sheng (or both) were happy yesterday.
  • Sandip enjoys watching Sheng cry, so Sandip is happy today only if Sheng was sad yesterday.
  • Tracy is happy today only if Tracy was happy yesterday, meaning she has an independent streak.

Suppose that on day 1, all four of the friends are sad. After a few days, the friends reach a stable emotional state that repeats itself. What is the emotional state of each person in this repeating state?


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