If n = 1 + x, where x is the product of 4 consecutive positive integers, then which of the following is/are true?
1. n is odd;
2. n is prime
3. n is a perfect square

Let's assume $$x$$ to be product of $$a, a+1, a+2,$$ and $$a+3$$

Hence, $$x=a(a+1)(a+2)(a+3)$$

$$n=a(a+1)(a+2)(a+3)+1$$

$$n=a(a+3)(a+1)(a+2)+1$$

$$n=(a^2+3a)(a^2+3a+2)+1$$

Let's assume$$a^2+3=p$$

$$n=p(p+2)+1$$

$$n=p^2+2p+1$$

$$n=(p+1)^2$$

Hence, we can say that n is a perfect square. 

Hence, 3 is true and 2 is automatically false as perfect squares can't be prime. 

Product of any 4 consecutive integers is always even, as one of the numbers among the 4 consecutive integers will be even and any number multiplied by an even number is even. x is even, hence x+1 is odd. thus n is odd. 

Hence both 1 and 3 are true.