On the Subject of Nifty Numbers

Hexatrigesimal is a bit of a mouthful. Let's just call it base-36 instead. Wait, what base is the 36 in?

This module presents two displays. The top display shows four digits, the bottom five. Each digit has two buttons to raise or lower it. There is also a larger button on the right labeled with either a plus or a minus.

  • To disarm the module, take the bomb's serial number and split it through the middle into two equal halves of three characters each.
  • Each half represents a three digit number in base-36.
  • If the large button displays a plus, add the two numbers together. If the large button displays a minus, subtract the smaller number from the larger.
  • Enter this number, still in base-36, into the top display of the module.
  • Convert the number to base-10, and enter this number into the bottom display.
  • Press the large button to submit the answer. If both numbers are correct, the module will solve.

Base-36 Information

A base is the number of digits that a (positional) counting system uses to represent numbers. The most common base is base-10 or decimal, which uses 10 digits to represent numbers: 0-9.

Base-36 uses 36 digits. Conveniently, these digits can be represented using exactly all of the Arabic numerals 0-9, followed by the Latin letters A-Z, such that A = 10, B = 11, all the way up to Z = 35.

To represent larger numbers, the numbers of a base will need to be combined into a multi-digit number. In base-10, each additional digit represents a larger power of ten. For example, the number 263 means 2×100 + 6×10 + 3×1.

In base-36, instead of a ten's, hundred's (10×10), thousand's (10×10×10 or 10³) etc. place, there is a 36's, 1296's (36×36), 46656's (36×36×36 or 36³), etc. place. Therefore, the number 263 in base-36 means 2×1296 + 6×36 + 3×1 = 2811, and the number L8W means 21×1296 + 8×36 + 32×1 = 27536 in base-10.

Adding and subtracting works exactly the same way in base-36. Be sure not to forget to carry a digit to another column if needed. For example: 9 + C = L, Z + 1 = 10, RN + Z = SM, 3Q + F = 45, Q - A = G, 1B - D = Y