Level 4: Math Homework
discussion to follow. May not be suitable for children under the age of
I created this composition by a process derived from one of
my favorite methods of killing time on the subway - Ken Ken. It also
be a great educational tool for teaching math, problem solving, and
thinking. Japanese math teacher Tetsuya Miyamoto invented Ken Ken in
2004. This Sudoku-like puzzle involves
square grid with digits 1 through however many rows and columns are in
puzzle (3x3, 4x4, 5x5 ... , 9x9). By using arithmetic facts and logical
thinking, each puzzle has a unique arrangement of digits in the grid.
I picked a 5x5 puzzle at random to solve.
= 5 beats in
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
puzzle for each subsequent logical step
represents the blank puzzle at the start. The second measure represents
the digits I could place in one logical step. The third measure
digits I could place based on the deductions I could make following the
logical step. The process continues until the penultimate measure,
represents the completed puzzle with a digit in every square. The final
is the sustained tonic note, signaling victory.
one point in the
piece you'll hear are two simultaneous notes on two adjacent pulses,
represents that I had narrowed down the choice for two boxes to one of
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
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.