Sum of first n natural numbers is n(n+1)/2. The sum of the array, represented by s, is n(n+1)/2 - x + y (subtract x - the missing number and add y - the duplicated number) gives:

1: n(n+1)/2 - x + y = s

Product of first n natural numbers is represented as: n! The product of the numbers in array is p.

2: p x / y = n!

(multiply by x - add missing number to product and divide by y - remove duplicated number from product).

If a is duplicated and b missing, computing the sum and the product of all the numbers can give you a-b and a/b, from which you can deduce a and b.