After the round in the posed problem, it reaches a stalemate. If Peter had said "I don't know the numbers" at the end there, Sandy can exclude the possibility

After the round in the posed problem, it reaches a stalemate. If Peter had said "I don't know the numbers" at the end there, Sandy can exclude the possibility that the numbers were 77 and 84. However, at this point Peter already knows that Sandy still doesn't know the numbers: Even if the sum Sandy was told was 161, there are still five remaining live possibilities for that sum (62 + 99, 65 + 96, 70 + 91, 76 + 85 and 80 + 81), so Peter gains no new information from Sandy's next statement that Sandy does not know the numbers.