While interesting, I don’t think our protagonist is particularly bright given her supposed age. For one it would be REALLY easy to determine which day was chosen. She just needs to keep a journal and mark down a number for each day. Which ever number is kept when the next day comes around is the day that was chosen.
Also, it would be actually pretty easy to prove what’s happening with the help of 1 other person. This person wouldn’t even have to know about her condition. Simply ask them to generate an word file with a ton of randomized words. The next day after the word file is generated she’ll ask to be told a specific number word in the sequence. Whenever a day is chosen she can reiterate all the words she learned from the days that weren’t chosen, proving she has information she couldn’t have.
the first idea is good, i think, but as for the second, how would anyone but her know what the correct strings of words from non-chosen days were in order to check?
The person who generated the list would know. They would generate the list a day before beginning the experiment so that it would remain fixed.
The first one sounds like a possibly good idea, but as for the second one, I'm curious as to how Ayaka would convince someone to accept her rather odd request without explaining her condition. Considering what happened when she tried explaining it to her mother, and that she doesn't have anyone who trusts her implicitly enough to listen to such a request, I'm not surprised that she gave up on the idea of people believing her. As such, I think judging her as not "particularly bright" based on this oversight is a bit harsh.
Personally, it's a bit of a pet peeve of mine when viewers of fictional media who are able to watch the story dispassionately, with the benefit of time to digest what they've seen and knowledge of the consequences of characters' choices, second-guess decisions made by characters in the story, who may not know as much as the viewers do and/or may have emotional baggage that affects their decisions. It's personally more than a little odd that viewers who take all that effort to think of the things a character should have done seldom take the time or effort to see things from the character's perspective.
Incidentally, I have to wonder if fiction like Groundhog Day exists in this series' universe. For all Ayaka knows, not only are there no other people like her, but no one has even imagined the concept of a person who relives each day multiple times.
Sorry if this sounds like a rant; as I said, this is a pet peeve of mine.