Arcade machine doesn't come up t=with select start position so i cant complete it

Hi! I'm playing through Castle Claymount, lovely game, and I got up to the point where you input 328 into the cash register machine, but the game won't accept my answer. I saw some forums saying you have to put the hat on the goose and inspect the periodic table, but I have done both those things and it still will not work. I would really appreciate some tips on how I can get the game to accept my answer....

I just got through the puzzle involving a curly-figure contraption, and two signs indicating the equation "Goose + Egg" and "Goose = <math>". I was confounded by this one for a long time, and ended up looking up 3 hints. This gave me the answer I could input, but I still can't figure out how it draws that conclusion. I can still move on with the game now, but can anyone answer how "egg = 315"? Otherwise all the puzzles have been really satisfying and tricky! Enjoying it all so far....

I'm unsure if I'm just tired since I started that puzzle the second time i was angry or had to hurry a bit, but here I am not getting what the hints or the game wants from me there. I spammed hint the last time I was kinda bored or annoyed at something. Okay still not sure what I'm not understanding here, but I managed to understand the hint a little bit later....

I'm probably the only person to play this game on a Steam Deck and can confirm it works great, and I did not notice any issues during my play through. Additional information: Played on the 1TB OLED model, no modifications.