The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6² + 7² + 8² + 9² + 10² + 11² + 12².

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is 4164. Note that 1 = 0² + 1² has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than 10⁸ that are both palindromic and can be written as the sum of consecutive squares.

+-#Enumerable
module Enumerable
  def sum
    self.inject{|u,v|u+v}
  end
  def product
    self.inject{|u,v|u*v}
  end
  def count(ob)
    self.select{|i|i==ob}.length
  end
  def take_while
    return [] unless yield(self.first)
    if(self.class==Range)
      evalPoint=self.first
      evalPoint=evalPoint.succ while yield(evalPoint.succ) and not evalPoint==self.last
      return self.first..evalPoint
    else
      s=self.to_a
      upTo=1
      upTo+=1 while yield(s[upTo]) and upTo<self.length
      return self[0...upTo]
    end
  end
end

+-#isPalindrome?
def isPalindrome?(n)
  s=n.to_s
  s==s.reverse
end

def p125
  limit=10**8
  ans=Set.new
  low=1
  until (low**2+(low+1)**2)>=limit
    high=low+1
    s=low**2+high**2
    until s>=limit
      ans.add(s) if isPalindrome?(s)
      s+=(high+=1)**2
    end
    low+=1
  end
  puts ans.sum
end