by Dan Katz
Problem: Arbor Day Town/​Bloomsday Town

The students who submitted these exam sheets don’t seem to have answered the questions very accurately. It’s not a bad idea to start by figuring out what the answers should have been:

  1. A (Nile Rodgers)
  2. E (the Congress Street Bridge)
  3. D
  4. B
  5. A (Stranger Things)
  6. C (the “buttered toast phenomenon”)
  7. D (the Dancing Men cipher)
  8. B (so that he could copyright the trick)
  9. E
  10. D
  11. D (the Schmuzzies)
  12. E (Orange Orange)
  13. A
  14. D (in the film Upside Down)
  15. A (Rage Against the Machine)
  16. E
  17. A
  18. C (the Inverted Jenny has two 24’s to indicate value and a 38262 on the plane itself)
  19. B (Curious George)
  20. C
  21. A (she sells her house and buys a farm before the third book begins)

Here are the exam sheets again for reference:

Looking more closely at the rather tactless comments left by the grader, the capital letters in the given order spell COMBINE, which suggests we should combine the content of the seven exam sheets onto one. This is worth trying, but it yields the following, which doesn’t obviously provide any information (and any temptation to read the result in 5-bit binary should hopefully be discouraged by the 27 in row 4):

Without any other clear way to proceed, it might occur to the solver to check the grader’s work. Doing so reveals that the 2nd, 5th, and 7th exams have the correct percentage of correct answers written down, but the others do not; the percentages imply that they should have 5, 5, 9, and 5 correct answers respectively, but instead they have 7, 11, 6, and 8. What happened? A hint to what’s going on lies in the content of the exam questions, every one of which relates to either the phrase “upside down” or an instance of an object or person being upside down:

  1. The lead single from the album was “Upside Down”
  2. Bats sleep “upside down”
  3. Blizzards are sometimes turned upside down before serving to demonstrate their thickness
  4. Lloyd hangs from the rope upside down
  5. The Demogorgon lives in a world the kids refer to as The Upside Down
  6. The phenomenon claims that the toast tends to land upside down
  7. The men in both cipher letters are upside down
  8. Houdini hangs upside down when performing the trick
  9. The song, “Yorktown,” has the subtitle and refrain “The World Turned Upside Down”
  10. Parrying the card reverses gravity so that Cuphead is upside down
  11. The characters are from The Upside Down Show
  12. Orange Orange used to be named Upside Down
  13. This work was famously accidentally hung upside down
  14. The film is called Upside Down
  15. The band got in trouble for hanging American flags upside down
  16. The couple are eating pineapple upside down cake in this scene
  17. One of the principal villains is Upside Down Man
  18. This stamp is famous for featuring an upside down picture of a plane
  19. The lead single from the album was called “Upside Down”
  20. The award was for the scene in which Spider-Man kisses Mary Jane while hanging upside down
  21. She lives in an upside down house

This pattern, along with the “SCANOMATIC” logo implying the exams were computer-graded, suggests turning the incorrectly graded exams upside down (rotating them 180 degrees, not reflecting vertically) and grading them as if they were right side up in that orientation; the inverted exams now have the correct percentage of questions right, so they must have been entered into the grading machine upside down, as shown:

Having turned these exams to reflect what was graded, it may be time to “combine” again, which results in the following overlap:

This is still not crystal clear, but the F near the top stands out (in the same orientation as the grader comments) and this will hopefully convince the solver to rotate the array 90 degrees counterclockwise and read one letter in every three columns. Doing so reveals the puzzle’s answer, FLUNKED. (Note: The F and L are capitalized to improve legibility, particularly since every column must have at least one filled-in bubble. No statement about the educational standards of the state of Florida is implied by this puzzle. Voting machine standards, maybe.)