Sudoku solver by backtracking algorithm

sudoku-solver-bt.rb

require 'matrix'

class Matrix
  # Assign the given value to the slot at the specified row and column
  def []=(row, column, value)
    @rows[row][column] = value
  end
  def to_s
    [sprintf("%d x %d Matrix", @rows.length, column_size),
      @rows.map { |row| row.inspect }].flatten.join("\n")
  end
end

grid = Matrix.rows([
  [8,0,0,0,0,0,0,0,0], 
  [0,0,3,6,0,0,0,0,0], 
  [0,7,0,0,9,0,2,0,0], 
  [0,5,0,0,0,7,0,0,0], 
  [0,0,0,0,4,5,7,0,0],
  [0,0,0,1,0,0,0,3,0],
  [0,0,1,0,0,0,0,6,8],
  [0,0,8,5,2,0,0,1,0],
  [0,9,0,0,0,0,4,0,0]
  ])

  puts grid

def solve_sudoku(grid)
  return true if grid.index(0).nil?
  
  actual = grid.index(0)
  (1..9).each do |n|
    next if grid.row(actual[0]).include?(n) || grid.column(actual[1]).include?(n) || verify_blocks(grid, actual, n)
    grid[actual[0], actual[1]] = n
    if solve_sudoku(grid)
      return true
    end
  end
  grid[actual[0], actual[1]] = 0
  return false
end

def verify_blocks(grid, actual, value)
  block_row_start = actual[0] - (actual[0] % 3)
  block_column_start = actual[1] - (actual[1] % 3)
  block_row_end = block_row_start + (3 - 1)
  block_column_end = block_column_start + (3 - 1)
  (block_row_start..block_row_end).each do |r|
    (block_column_start..block_column_end).each do |c|
      return true if grid[r,c] == value
    end
  end
  return false
end

solve_sudoku(grid)
puts grid