We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.



In [4]:

    
39 * 186









    Out[4]:





7254



In [5]:

    
12345.to_s









    Out[5]:





"12345"



In [6]:

    
12345.to_s.split("")









    Out[6]:





["1", "2", "3", "4", "5"]



In [7]:

    
123456789.to_s.split("")









    Out[7]:





["1", "2", "3", "4", "5", "6", "7", "8", "9"]



In [8]:

    
target = 53241

123456789.to_s.split("").map { |item| target.to_s.split("").count(item) <= 1 }









    Out[8]:





[true, true, true, true, true, true, true, true, true]



In [9]:

    
123456789.to_s.split("").all? { |item| target.to_s.split("").count(item) <= 1 }









    Out[9]:





true



In [88]:

    
def pen_digital?(target)
  return false if target.to_s =~ /0/
  return 123456789.to_s.split("").all? { |item| target.to_s.split("").count(item) <= 1 }
end

pen_digital? 12345









    Out[88]:





true



In [89]:

    
pen_digital? 29382









    Out[89]:





false



In [90]:

    
def pen_digital_string?(target)
  return false if 123456789.to_s.split("").all? do |item|
    target.tr("*=", "").split("").count(item) <= 1
  end == false

  target =~ /(\d*?)\*(\d*?)=(\d*)$/
  return true if (($1.to_i * $2.to_i) == $3.to_i)
  return false
end



In [91]:

    
pen_digital_string?("123*123*1234")









    Out[91]:





false



In [92]:

    
39 * 186









    Out[92]:





7254



In [93]:

    
pen_digital_string?("39*186=7254")









    Out[93]:





true



In [16]:

    
pen_digital_string?("123*456=789")









    Out[16]:





false



In [98]:

    
def find_pen_digit_string32(num)
  return unless pen_digital?(num)

  result = []
  source = [1, 2, 3, 4, 5, 6, 7, 8, 9] - num.to_s.split("").map{|i| i.to_i}

  multiplicand = source.combination(3)
  multiplicand.each do |com|
    multiplier = source - com
    left = com.permutation(3).map{|a,b,c| [a,b,c]}
    right = multiplier.permutation(2).map{|a,b| [a,b]}

    strings = left.product(right).map do |arr|
      arr[0].join + "*" + arr[1].join + "=" + num.to_s
    end

    strings.each do |string|
      return num if pen_digital_string?(string)
    end
  end

  return 
end

find_pen_digit_string("1234")



In [99]:

    
find_pen_digit_string(7254)









    Out[99]:





7254



In [117]:

    
result = []

(4140..9876).lazy.each do |i|
  temp = find_pen_digit_string(i)
  result << temp if temp != nil
end









    Out[117]:





4140..9876



In [118]:

    
result









    Out[118]:





[4396, 5346, 5796, 7254, 7632]



In [119]:

    
result.inject &:+









    Out[119]:





30424



In [145]:

    
def find_pen_digit_string41(num)
  return unless pen_digital?(num)

  result = []
  source = [1, 2, 3, 4, 5, 6, 7, 8, 9] - num.to_s.split("").map{|i| i.to_i}

  multiplicand = source.combination(4)
  multiplicand.each do |com|
    multiplier = source - com
    left = com.permutation(4).map{|a,b,c,d| [a,b,c,d]}
    right = multiplier.permutation(1).map{|a| [a]}

    strings = left.product(right).map do |arr|
      arr[0].join + "*" + arr[1].join + "=" + num.to_s
    end

    strings.each do |string|
      return num if pen_digital_string?(string)
    end
  end

  return 
end

find_pen_digit_string41("1234")



In [146]:

    
result = []

(1234..9876).lazy.each do |i|
  temp = find_pen_digit_string41(i)
  result << temp if temp != nil
end









    Out[146]:





1234..9876



In [147]:

    
result









    Out[147]:





[6952, 7852]



In [148]:

    
30424 + 6952 + 7852









    Out[148]:





45228