q1.rb

s = 'FourscoreandsevenyearsagoourfaathersbroughtforthonthiscontainentanewnationconceivedinzLibertyanddedicatedtothepropositionthatallmenarecreatedequalNowweareengagedinagreahtcivilwartestingwhetherthatnaptionoranynartionsoconceivedandsodedicatedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWehavecometodedicpateaportionofthatfieldasafinalrestingplaceforthosewhoheregavetheirlivesthatthatnationmightliveItisaltogetherfangandproperthatweshoulddothisButinalargersensewecannotdedicatewecannotconsecratewecannothallowthisgroundThebravelmenlivinganddeadwhostruggledherehaveconsecrateditfaraboveourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorlongrememberwhatwesayherebutitcanneverforgetwhattheydidhereItisforusthelivingrathertobededicatedheretotheulnfinishedworkwhichtheywhofoughtherehavethusfarsonoblyadvancedItisratherforustobeherededicatedtothegreattdafskremainingbeforeusthatfromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwhichtheygavethelastpfullmeasureofdevotionthatweherehighlyresolvethatthesedeadshallnothavediedinvainthatthisnationunsderGodshallhaveanewbirthoffreedomandthatgovernmentofthepeoplebythepeopleforthepeopleshallnotperishfromtheearth'

longest = ''
(0...s.length).each do |i|
  (0..i).each do |j|
    part = s[j..i]
    longest = part if part == part.reverse && part.length > longest.length
  end
end

longest
=> "ranynar"

q2.rb

def is_prime? number
  (2..number/2).each do |i|
    return false if number % i == 0
  end
  true
end

def fib index
  return 0 if index == 0 
  return 1 if index == 1
  fib(index - 1) + fib(index - 2)
end

highest_prime = 1
index = 0
while highest_prime < 227000
  index += 1
  result = fib index
  highest_prime = result if is_prime?(result)
end

calc = highest_prime + 1

factors = []
while !is_prime? calc
  (2..calc/2).each do |i|
    if calc % i == 0
      factors << i if !factors.include? i
      calc = calc / i
    end
  end
end

factors.sum
=> 352

q3.rb

numbers = 3, 4, 9, 14, 15, 19, 28, 37, 47, 50, 54, 56, 59, 61, 70, 73, 78, 81, 92, 95, 97, 99
set_count = 0
numbers.each_with_index do |number, i|
  numbers.combination(i).each do |combination|
    set_count += 1 and puts combination.inspect if combination[0..-2].sum == combination[-1]
  end
end

set_count
=> 179