Basic Arithmetic Digit Equations (BADEs)

MathBabbler created a BAB on 7 December 2016 that remembered the bombing of Pearl Harbor on 7 December 1941. He had been pondering the creation of Digit Equations for most of 2016 and it was decided to use the number 1941 to introduce the topic of BADEs (Basic Arithmetic Digit Engineering).

Digit Equations in a nutshell: Every digit in a number must be used to find an equation. Each digit can be used only once. Math functions can be used on the digits. The digits can be used in any order in the equation; however, "classic" Digit Equations use the digits in the same order in which they are found in the number.

   1941 as the digits 1, 9, 4, 1

   equation:  1 * sqrt(9) = 4 - 1

More examples...

   24: digits are 2, 4
   equation: 2 = sqrt(4)

   238: digits are 2, 3, 8
   equation:  2^3 = 8

   2016: digits are 2, 0, 1, 6
   equation: (2 + 0 + 1)! = 6

   314:  digits are 3, 1, 4
   equation: 3 + 1 = 4

   82:  digits are 8, 2
   equation: cuberoot(8) = 2

   85283 (MathBabbler's zip code):  digits are 8, 5, 2, 8, 3
   equation: 8 + 5 = 2 + 8 + 3

   362:  digits are 3, 6, 2
   equation: 3 * 2 = 6

Similar to BARS and BADs, BADEs have "evals" (evaluations). BARS and BAD evals are Pi, Phi, 42, 37, age, and cardinality.

   1941:  1 + 9 * 4 * 1 = 37     [bade37Eval]
   1941:  (1 + sqrt(sqrt(9)! - 1) / sqrt(4) = Phi    [badePhiEval]
   1941:  9 - 4 - 1 / 1 = 4      [badeCardinalityEval]

   1942:  (1 + 9) * 4 + 2 = 42      [bade42Eval]
   1942:  9 * 4 + (1 + 2)! = 42     [bade42Eval]
   1942:  9 * 4 + 2 - 1 = 37        [bade37Eval]

The primary motivation for badeEvals is to make every number a BADE.


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 07 December 2016 (posted 31 December 2016)

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