index_locator.rb

#!/usr/bin/env ruby

def x_values
  %w(a b c d)
end

def y_values
  %w(m n o p)
end

def z_values
  %w(q r s t)
end

def identify_position(target_x, target_y, target_z)
  x_values.index(target_x) +
    (x_values.count * y_values.index(target_y)) +
    ((x_values.count * y_values.count) * z_values.index(target_z))
end

def identify_target(value)
  z_index = (value / (x_values.count * y_values.count))
  value -= z_index * (x_values.count * y_values.count)

  y_index = (value / x_values.count)
  value -= y_index * x_values.count

  x_index = value

  [x_values[x_index], y_values[y_index], z_values[z_index]]
end

puts identify_position('a', 'm', 'r').inspect
puts identify_target(16)