Neil chose two distinct integers from 1 to 9 inclusive.
He told Sam only the sum of these two integers, and Patrick only the product.
But Neil let both Sam and Patrick know that the numbers came from 1 to 9 inclusive.
The following conversation occurs:
Patrick: "I don't know the numbers."
Sam: "I don't know the numbers."
Patrick: "Now I know the numbers."
Sam: "But I still don't know the numbers."
Patrick: "Well, if it helps, the absolute difference between your number and my number is larger than 1."
Sam: "Now, I know the numbers too!"
Which of the following is definitely one of Neil's number?