Player A casts Scheming Symmetry in their turn and choses two of the other players (B and C) to have to resolve this. What is the correct way for this to happen, specifically related to Panglacial Wurm being found?
How should Scheming Symmetry resolve in Judge Tower (shared library) with a Panglacial Wurm that must be cast?
Rule 101.4 covers this type of interaction; while Scheming Symmetry theoretically resolves simultaneously as per rule 701.19i, the decision to cast Panglacial Wurm occurs in APNAP order.
This means that, while playing Judge Tower with either the "Players must treat every instance of “may” as “must”" or broader "Cards must be played as soon as legally allowed." rules, the first player in turn order from the active player that was targeted by Scheming Symmetry will be required to utilize the "you may" on Panglacial Wurm to cast it (during searching the library will also be required to be kept in order due to the ruling on Panglacial Wurm).
701.19i If multiple players search at once, each of those players looks at the appropriate cards at the same time, then those players decide in APNAP order (see rule 101.4) which card to find.
101.4. If multiple players would make choices and/or take actions at the same time, the active player (the player whose turn it is) makes any choices required, then the next player in turn order (usually the player seated to the active player’s left) makes any choices required, followed by the remaining nonactive players in turn order. Then the actions happen simultaneously. This rule is often referred to as the “Active Player, Nonactive Player (APNAP) order” rule.
Example: A card reads “Each player sacrifices a creature.” First, the active player chooses a creature they control. Then each of the nonactive players, in turn order, chooses a creature they control. Then all creatures chosen this way are sacrificed simultaneously.
Rule 701.19i describes more accurately to the context how multiple players searching at the same time is being resolved. Furthermore, as you can probably tell from my answer and the followup comment to it, I would like to see a rules quote if possible, or alternatively a statement about the rules you mentioned, which I cannot find at any public source anymore. May 1 at 0:31
1The judge tower website is still viewable via web.archive.org/web/20230309180113/http://judgetower.com/… , and has both the unlimited "Cards must be played as soon as legally allowed." rule and “may” as “must” listed as core rules; but there are multiple variations of the rules, it being a heavily casual format e.g. reddit.com/r/magicTCG/comments/r4w27e/… has the “may” as “must” rules listed as optional May 1 at 1:21
Very nice find, thanks! I still think that for the purpose of learning the judging aspects for it, this specific interaction is more harmful than helpful (and as such, I can imagine that the rules stated on MtG Wiki have been sensibly updated by the community), but this is by all means a good answer! May 1 at 8:17
While your question, especially before the edit, is a little vague, the only particularily interesting interaction here would be if a player could lose for not finding Panglacial Wurm.
There is a bit of an issue about the Judge Tower rules, with the seemingly official webpage only being reachable through archive.org (thanks KMR for the link), whereas all other versions that I can find in written form match the rules listed on MtG Wiki. For an answer relating to judgetower.com, see KMR's answer, whereas this answer handles rules as per the ones listed on MtG Wiki.
The rules do not actually require players to find and cast the Wurm, as only cards in hand have to be played, and the Wurm's ability isn't an activated ability, nor is a card in a library a card that player controls.
Therefore, while of course a player can choose to find that card, they are in no way required to. If they do choose to cast the creature, they have to cast it before choosing another creature to actually put on top of the library due to Scheming Symmetry, since they're only allowed to cast that card while searching their library (that is, if they choose to find a card at all).
1judge tower rules do require you to play panglacial wurm as if a card says may you must do it (from the judge tower website which does appear to be defunct now) and the ability does state "may cast" which in judge tower reads must cast. afaik that's standard for juge tower. the main issue here is the scheming symmetry is usually resolved simultaneously due to separate libraries but with a shared library it would be APNAP (I think) Apr 30 at 23:07
I was looking for distinct rules as the first part of writing my response. With the lack of anything like an "official" source, I chose the MtG Wiki as a source because of its community-editable format. Functionally identical rules can be found elsewhere, all mentioning that casting rules apply for cards in hand. I can easily see extending that to all cards in public zones, but as I already mentioned in my post, nothing mentions cards in hidden zones, nor do I see why it would. As I also said, I could see if people would disagree. I suggest to post your own answer, I can see that having merit. Apr 30 at 23:59
The 'Players must treat every instance of “may” as “must”.' rule is an optional extra, and is quite often included to make cards like Panglacial Wurm more interesting in the format May 1 at 0:31
1The possible inclusion of Panglacial Wurm in a judge tower deck does have effects beyond it's potential interaction with Scheming Symmetry, as if it is included the deck must be kept in order while searching. May 1 at 1:37