# The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9
# in some order, but it also has a rather interesting sub-string divisibility property.

# Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:

# d2d3d4=406 is divisible by 2
# d3d4d5=063 is divisible by 3
# d4d5d6=635 is divisible by 5
# d5d6d7=357 is divisible by 7
# d6d7d8=572 is divisible by 11
# d7d8d9=728 is divisible by 13
# d8d9d10=289 is divisible by 17

# Find the sum of all 0 to 9 pandigital numbers with this property.

start_time = Time.now

require 'prime'

def has_substring_property?(pandigital)
  return false if pandigital.to_s.length != 10
  substrings = []
  primes = Prime.first(7)

  (1..7).each do |index|
    substrings << pandigital.to_s[index..index + 2]
  end

  substrings.each_with_index {|substr, i| return false if substr.to_i % primes[i] != 0}

  true
end

pandigitals09 = (0..9).to_a.permutation(10).to_a.map {|digits| digits.join("").to_i}

pandigitals_with_curious_property = pandigitals09.select {|pan| has_substring_property?(pan.to_i)}

p pandigitals_with_curious_property.reduce(:+)

puts "Time elapsed: #{(Time.now - start_time)} sec"

# => 16695334890

# Takes 83 seconds to run on my machine, which is beyond the acceptable limit in my opinion.
# Let's refactor this one later.

Complete P43, but refactoring badly needed
Complete P43, but refactoring badly needed
