SAFE PASSWORDS

• ALPHABETICAL

  NUMERICAL

  SYSTEM

  DORM ROOM A

  LIES

  21 18 14 28

  BASE-36

  DORM ROOM B

  CAGE

  3175

  ??? →

  DORM ROOM C

  DARK

  096

  ???

• ALPHABETICAL

  NUMERICAL

  SYSTEM

  CAFETERIA

  LIFE

  C965

  BASE-16

  REC ROOM

  MIND

  14181323

  ??? ←

  MEETING ROOM

  TIME

  1016

  ???

CIPHER KEYS

• Normally a numbering system also known as hexatridecimal, in this instance Zero has used base-36 to mark certain doors that will be locked until their associated HETU's puzzle has been completed to differentiate them from the numbered doors, at least one of which will be beyond the marked door. To introduce the players to the concept, they also used hexatridecimal in Dorm Room A's safe code.

  The reason for the usage of base-36 for this becomes evident once observed like so, with the green top lines being the base-36 equivalents of the decimal numbers in the white bottom lines:

  0 1 2 3 4 5 6 7 8 9 A  B  C  D  E  F  G  H  I  J  K  L
  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  10 11 12 13
  22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

  14 15 16 17 18 19 1A 1B 1C 1D 1E
  40 41 42 43 44 45 46 47 48 49 50

  However, as Zero has no use for the numbers 1 through 9, nor any number past Z, the usage of hexatridecimal in the Nonary Game can be reduced to only the part concerning the alphabet:

  A  B  C  D  E  F  G  H  I  J  K  L  M  
  10 11 12 13 14 15 16 17 18 19 20 21 22

  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
  23 24 25 26 27 28 29 30 31 32 33 34 35

• Normally a numbering system also known as hexadecimal, in the Nonary Game it will be used as a means of encoding certain things. To compare it to a more familiar numbering system: base 10, or the term likely more familiar to you, decimal, regard your hands, palms-down. Lower each finger while counting them, from your left pinky to your right, until you make a fist. Now begin counting from 11, and raise each finger back up. You will reach 20 when your hands have fully opened again.

  Now, imagine you had 8 fingers per hand instead, with the additional fingers located past your thumb. Do the same as before, and simply imagine lowering the 6 extra fingers, then once again reverse this process.

  Written and pronounced in decimal, you would have hit 16 (sixteen) when your hands closed, and 32 (thirty-two) when they were open again. However, the hexadecimal representation of the numbers you counted to would be 10 (tex) when your hands closed and 20 (twentex) when they were open again.

  Additionally, during the second exercise, the point at which you counted your 15th (fifteenth) finger was the point at which you would count your Fth (fimth) finger in hexadecimal.

  This is because there are, of course, only 10 Arabic numerals (from 0 to 9). Thus, to represent single-digit numerals past 9, hexadecimal uses letters A through F of the Latin alphabet, like so:

  0 1 2 3 4 5 6 7 8 9 A  B  C  D  E  F
  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  0 1 2 3 4 5 6 7 8 9 A  B  C  D  E  F 10 11 12 13 14 15
  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

  
  

  0 1 2 3 4 5 6 7 8 9 A  B  C  D  E  F  10 11 12 13 14
  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

  15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 25 26 27 28
  21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

  As for safe codes using hexadecimal, only having access to letters A through F is rather limiting when it comes to spelling out words. But theworkaround is quite obvious, isn't it?

  1  2  3  4  5  6  7  8  9  A  B  C  D
  A  B  C  D  E  F  G  H  I  J  K  L  M  

  E  F  10 11 12 13 14 15 16 17 18 19 1A
  N  O  P  Q  R  S  T  U  V  W  X  Y  Z