I LOVE TO EAT DUCKS!!
Two ducks, Wat and Q, are taking a math test with 1022 other ducklings. The test has 30 questions, and the nth question is worth n points. The ducks work independently on the test. Wat gets the nth problem correct with probability 1/ n2 while Q gets the nth problem correct with probability 1/ n+1 . Unfortunately, the remaining ducklings each answer all 30 questions incorrectly. Just before turning in their test, the ducks and ducklings decide to share answers! On any question which Wat and Q have the same answer, the ducklings change their answers to agree with them. After this process, what is the expected value of the sum of all 1024 scores?