MongoDB puzzle

gistfile1.rb

n = rand(10) + 2
list = (1..n).to_a.shuffle
list[1 + rand(list.length - 1)] = list.first
puts list.join(", ")
a = n * n.succ / 2
b = n * n.succ * (2 * n).succ / 6
a2 = list.inject(:+)
b2 = list.inject(0) { |acc, x| acc + x * x }
missing = ((b2 - b) / (a2 - a) - a2 + a) / 2
duplicate = a2 - a + missing
puts "missing: #{missing} duplicate: #{duplicate}"