number_search.rb

# five digit number
# two of the digits are the same
# four of the digits are odd
# number is higher than 40010
# number is higher than 45000
# digit sum is 16

# five digit, upper/lower bounds
candidates = (40011..44999).select { |i| 
  # two digits are the same
  digits = i.to_s.split("")
  digits.uniq.size == 4
}.select { |i|
  # digit sum
  i.to_s.split("").map(&:to_i).inject(:+) == 16
}.select { |i|
  # four digits are odd
  digits = i.to_s.split("").map(&:to_i)
  digits.count(&:odd?) == 4
}

candidates
# => [41137,
#     41173,
#     41317,
#     41335,
#     41353,
#     41371,
#     41533,
#     41713,
#     41731,
#     43117,
#     43135,
#     43153,
#     43171,
#     43315,
#     43351,
#     43513,
#     43531,
#     43711]