I think that answer was poorly phrased because those possibilities are eliminated in a sense. There is a better answer further in the thread that explains "If the solution was not one of the flipped triplets, then the first player would not have worked out the solution." Thus if it was one of your other infinite triplets (eg. 65, 12, 53) then round 2 player 1 would've still answered 'I don't know'. Since they did respond with a definitive answer it had to be one of the formula solutions, since those were the only solutions they could prove. And since the only formula with a factor in 65 is 5 the correct formula must be [5A, 2A, 3A] and thus [65, 26, 39].

You should be able to generate an infinite number of these problems just by multiplying the first formula factor by a prime number. Like the same question but the person answers '52' restricts you to either [4a, 3a, a] or [4a, a, 3a]. Since the question only asks for the product of all the terms the answer is 4 * 13 + 3 * 13 + 13 = 104.