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 Sudokulike 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 15 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 15 AND
in the logical order of steps I took to fill it out.
