Twosquare (solution)

by Seth Schoen

These two squares are a magic square and a Latin square. Naturally, the magic square needs to be filled with magic, and the Latin square needs to be filled with Latin.

The magic square

To help you find the necessary structure, the magic square is presided over by Dariel Fitzkee, whose 1944 book The Trick Brain gives what would later be termed an occurrence classification of magic tricks into 19 numeric categories:

  1. Production
  2. Vanish
  3. Transposition
  4. Transformation
  5. Penetration
  6. Restoration
  7. Animation
  8. Anti-gravity
  9. Attraction
  10. Sympathetic Reaction
  11. Invulnerability
  12. Physical Anomaly
  13. Spectator Failure
  14. Control
  15. Identification
  16. Thought Reading
  17. Thought Transmission
  18. Prediction
  19. Extrasensory Perception

Each of the magic tricks given is best classified into one of these categories, giving the numbers 1-16, which must be arranged into a magic square so that each row, column, and diagonal sums to 34.

The Latin square

The Latin square is presided over by Latin enthusiast Carolus Linnæus, whose 1735 book Systema Naturae introduced the familiar Linnaean taxonomy. The original version included both the living and nonliving parts of the “empire of nature”, comprehending three regna ‘kingdoms’: Regnum Animale, Regnum Vegetabile, and Regnum Lapideum. This is the origin of the question animal, vegetable, or mineral?

Each of the sixteen Latin nouns belongs to one of these three kingdoms, or to none of them (the category called “abstract” in Twenty Questions). Also, each of the nouns is in one of the first four declensions.

The nouns must be arranged into a Latin square so that each row and each column contains each kingdom exactly once and each declension exactly once. (This use of a Latin square was inspired by the puzzle Isn’t It Romantic? from the 2000 MIT Mystery Hunt.)


Click here to see the completed squares.

Now, we can take the given letters for the magic square and the first letter of each Latin word to get:


Adding the letters in matching cells (A+A=B, wrapping around the end of the alphabet so that A+Z=A) gives


Reading the contents of the resulting square gives the answer, DUCKBILL PLATYPUS.

William S. Bergman
William S. Bergman