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In the fine movie The Martian astronaut Mark Watney is stranded on Mars and must devise some way to communicate with NASA and Earth. He manages to get the old Pathfinder vehicle (launched December 4, 1996; landed on Mars July 4, 1997; last communication September 27, 1997) working so that it is again in radio communication with Earth. Behind the scenes this takes a major effort by software engineers at JPL as the deep space communications networks have changed radically in 40 years.


The problem posed in the book is that Pathfinder can only send photos (and slowly at that) while Earth can only send commands to swivel the camera (a 360 degree panorama shown below).


Mark Watney concludes having the camera point to one of 26 characters of the English alphabetic (plus a question mark) would allow only (360 degrees / 27) ~13 degrees between letters. He decides this is too likely to be inaccurate so he opts for hexadecimals (0-9 plus A-F). Sixteen characters plus a question mark is seventeen so 360/17  ~21 degrees.  This also allows Earth to send other useful characters like numbers, although it takes two camera movements to represent a character. I am not entirely sure how sending two 3s (the number 3), two 4s (the letter D); two 5s (the letter U); two 6s (the letter f) or two 7s (the letter w) would be achieved.