5. Ken Ken 5x5
Level 4: Math Homework
(Warning: Nerdy discussion to follow. May not be suitable for children under the age of 35)

I created this composition by a process derived from one of my favorite methods of killing time on the subway - Ken Ken. It also happens to be a great educational tool for teaching math, problem solving, and logical thinking. Japanese math teacher Tetsuya Miyamoto invented Ken Ken in 2004.  This Sudoku-like puzzle involves filling a square grid with digits 1 through however many rows and columns are in the puzzle (3x3, 4x4, 5x5 ... , 9x9). By using arithmetic facts and logical thinking, each puzzle has a unique arrangement of digits in the grid.

The composition process:
I picked a 5x5 puzzle at random to solve.

= 5 beats in each measure represent the 5 rows in the puzzle
= 5 pulses for each beat represent the 5 columns
= 5 notes of a pentatonic scale represent the digits 1-5 to be placed over each of the 25 pulses
= measures of 5 beats (25 pulses) represent the state of my progress in solving the puzzle for each subsequent logical step

The first measure represents the blank puzzle at the start. The second measure represents all of the digits I could place in one logical step. The third measure represents the digits I could place based on the deductions I could make following the first logical step. The process continues until the penultimate measure, which represents the completed puzzle with a digit in every square. The final measure is the sustained tonic note, signaling victory.

At one point in the piece you'll hear are two simultaneous notes on two adjacent pulses, which represents that I had narrowed down the choice for two boxes to one of two digits, but I wasn't sure of their order. This "chord" finally resolves to single notes (digits) towards the end of the piece.

Challenge to Ken Ken masters:
Assemble a 5x5 Ken Ken puzzle that would correspond with this piece in both the final placement of the digits 1-5 AND in the logical order of steps I took to fill it out.