#1
largest_num = 0

(1..999).each do |i|
	(2..999).each do |j|
		if (i*j).to_s == (i*j).to_s.reverse
			largest_num = i*j if i*j > largest_num
		end
	end
end

puts largest_num

#2
ans = 1
(1..20).each do |i|
	ans = (ans * i)/ans.gcd(i)
end
puts ans

#3
(1..1000).each do |a|
	(2..1000).each do |b|
		c = 1000 - a - b
		if a**2 + b**2 == c**2 && b > a && c > b
#			puts a,b,c
			puts a * b * c
		end
	end
end