North Carolina, USAI've been away from speedrunning for a while, so my apologies for the delayed response. I believe this is the Namco Arcade Archives for PS4 you're talking about, so this is actually a port of the arcade version. I would imagine you could submit a run to the Arcade category using the PS4 version, but I defer to FlannelKat on this one as she's primarily involved in the arcade version, and there may or may not be differences with this port.
Since I am currently de-rusting Mystic Quest, I just wanted to pop in here and give my story. I also am in possession of an FFMQ cart where the resistance glitch does not work.
Fortunately I have a second cart on hand where the resistance glitch does work. Both of these carts appear to be the version where you can press Start+Select in the menu and get a readout of your SNES chip data.
Very interesting as both copies have a ROM chip with "SNS-MQ-0" printed on them. I'm not familiar enough to know if this means both are v 1.0 carts, but I assume this is the case. The MOSEL chip below the ROM chip has a slightly different value printed on each cart, but this may just be manufacturer's serial numbers. Perhaps one of these carts is just cursed.
Also from the SDA Knowledge Base:
"The glasses are the only known item that can be taken multiple times from the inventory. Depending on what's been triggered in the game (based on taken items and events), you can reach an area of memory that can trigger certain events or allow you to reach items from different rooms."
In this case, being able to take the Glasses multiple times is a programming oversight, and the player is reaching pretty far outside of what the developers intended and mucking with memory by doing so.
My thoughts concerning the Sphinx and the Broom:
A glitch can be defined as a problem or oversight in code affecting the function of a program or otherwise producing results that were not intended by the developer.
The Sphinx in Shadowgate functions as follows (from the SDA Knowledge Base): "The riddle you'll receive from the sphinx is chosen from six items based on the frame you speak to the sphinx. This makes it incredibly difficult to reliably get a specific riddle; however, the current question remains the same until you speak to the sphinx while his question is marked as answered. You can answer the current question correctly multiple times. The default value is the broom. This means you can enter the Sphinx's room, present the broom, and pass the sphinx without triggering the question. "
Bearing the above definition of a glitch in mind, answering the Sphinx with the Broom without talking to him first isn't necessarily a glitch since he is functioning the way the developers intended at the code level. You're simply exploiting his behavior by not giving him a chance to randomize the correct answer.
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Concerning the opening the Star Map, I feel like this is just a question of hitboxes, with the Star Map's hitbox being just slightly larger/lower than the Star's, enabling you to click it without picking up the Star first.
