in1.txt

0   0  2 21  2 23 15 18
4  22 24 17 12  4 11 19
3   3 11 15  5 12  6  8
18 23  6 12 18 24 15 11
9   7 19 18 16 18 14 18
2  17 10  6  5  7 20  7
5  24  5 24 18  0  1  3
24 21  6  8 21 23 18 13

in2.txt

12 7 11 4 22 22 17  6
15 24 2 1 9 8 16 20
11 23 15 9 17 6 24 4
23 21 3 4 8 17 22 17
6 6 22 16 2 5 8 1
11 10 17 2 8 18 14 10
7 11 24 3 13 10 15 7
20 20 3 1 9 7 10 6

in3.txt

2 13 20 9 19 8 16 12
22 15 16 14 14 11 12 5
13 12 3 6 4 12 8 15
4 21 8 18 17 13 5 1
9 14 15 19 15 4 4 2
16 6 16 4 11 16 3 17
3 15 15 3 15 14 8 21
22 19 16 24 0 19 8 22

main.rb

WIDTH = 8
def each_path(board, visited, i, j)
  dead_end = true
  [{dx: 1, dy: 0},
   {dx: -1, dy: 0},
   {dx: 0, dy: -1},
   {dx: 0, dy: 1}].each do |direction|
    new_j, new_i = direction[:dx]+j, direction[:dy]+i
    next if new_j < 0 ||
            new_i < 0 ||
            new_j >= WIDTH ||
            new_i >= WIDTH ||
            !visited[(v = board[new_i*WIDTH+new_j])].nil?
    dead_end = false
    visited[v] = true
    each_path(board, visited, new_i, new_j) { |*args| yield(*args) }
    visited.delete v
  end
  yield(visited, i, j, dead_end)
end

def search_longest_path(board)
  min_visited, max_visited = [], []
  (0...5).each do |i|
    (0...5).each do |j|
      each_path(board, {}, i, j) do |visited, i, j, dead_end|
        max_visited = visited.dup if visited.length > max_visited.length
        min_visited = visited.dup if min_visited.empty? || (dead_end && visited.length < min_visited.length)
      end
      puts "progress: #{i} #{j} #{max_visited.size} #{min_visited.size}"
    end
  end
  [min_visited.keys, max_visited.keys]
end

board = $stdin.read.scan(/\d+/).map(&:to_i)
fail if board.size != 64
min, max = search_longest_path(board)
puts "min: #{min.length} #{min.join(" => ")}"
puts "max: #{max.length} #{max.join(" => ")}"