TABLE = [
    [0,3,1,7,5,9,8,6,4,2], [7,0,9,2,1,5,4,8,6,3],
    [4,2,0,6,8,7,1,3,5,9], [1,7,5,0,9,8,3,4,2,6],
    [6,1,2,3,0,4,5,9,7,8], [3,6,7,4,2,0,9,5,8,1],
    [5,8,6,9,7,2,0,1,3,4], [8,9,4,5,3,6,2,0,1,7],
    [9,4,3,8,6,1,7,2,0,5], [2,5,8,1,4,3,6,7,9,0]
]

def damm_valid?(n) = n.digits.reverse.inject(0){|idx, a| TABLE[idx][a] } == 0

[5724, 5727, 112946].each{|n| puts "#{n}: #{damm_valid?(n) ? "" : "in"}valid"}