On the Subject of Dyscalculators

E, J, R. Easy as 5, 9, 2. Or simple as fa-do-ti.

• On the module is an upside-down calculator which can perform the four basic operations.
• However, there are errors consistently affecting the results of the calculations:
  1. The numeric values of the digits 0-9 are scrambled: this affects both the inputs and outputs of any calculation.
  2. Each operator has one of two errors:
     • +: The digits of both inputs are reversed before summing
       or the digits of the sum are reversed.
     • -: The digits of the both inputs are reversed before subtracting
       or the digits of the difference are reversed.
     • ×: The first five digits of the product
       or the last five digits of the product.
     • ÷: The remainder is prepended to the quotient
       or the remainder is appended to the quotient.
  3. The functions of the four operators are also scrambled.
  4. Stuck buttons:
     • Operator buttons cannot be pressed until the first operand has at least three distinct digits.
     • The first operand can have up to five total digits.
     • Digits that were entered into the first operand cannot be entered into the second.
     • The second operand may only consist of three distinct digits.
• To disarm the module, the correct passcode must be submitted by pressing equals instead of an operator, this may be done at any time the first operand has at least one digit.
• The passcode is equal to the result of the calculation corresponding to the first character of the serial number, after all errors are applied.