I don't have access to the Apprentices book at the moment, and I am trying to make up an Apprentice Gauntlet for a Tytalus (though conceivably for Flambeau or Ex Miscellanea). Does the following sound reasonable.
Master tells apprentice it is a treasure hunt, and must acquire specific items from 7 locations and reach the finish line with all of them by a certain time. Here is the directions to the first one. When you acquire that, there will directions to the next "treasure". Also here is some casting tablets for spells that may help (at least one is needed). Use wisely, as each casting will cause you quit a lot of fatigue. And go!
There will be puzzles to solve and spells to cast at each stage. As the observing Quaesitore is told, the treasure hunt can be achieved without violating the Code, be it interfering with mundanes, molesting the fae, or depriving a mage (coincidentally an enemy) of their magical resources.
Extra bonus - the teleportation casting tablet is the flawed version of the spell the master first invented with experimentation - it absolutely will not transport Animal material. A fact the apprentice will learn after using it and arriving without leather boots and coat, his lunch in the wallet will be missing ham and cheese, and only the contents of the leather wine/water skin will travel.
Extra bonus - two apprentice gauntlets are happening. The second apprentice has to catch and stop the first apprentice. The first apprentice has an hour's head start.
This sounds like a rather typical Flambeau gauntlet. I am sure it could fit many magi of other houses, with some variation in the kind of treasures, locations, and obstacles.
However, I have the impression that Tytalus do not stage their gauntlets, but expect the apprentice to just rise to the challenge and get there. Well I suppose your example works, as a long as it is not presented to the apprentice for what it is but more like an everyday assignment.
Page 83 in HoH:S has info on the apprentice's gauntlet for house Tytalus.
It usually involves some sort of contest between master and apprentice, with the goal of the apprentice being to get their master to acknowledge them as an equal.
You could combine the two. It's a treasure hunt, but the twist is it's impossible. Passing the gauntlet consists of (a) coming back and explaining in detail your opinion of your master, optionally swearing revenge; or (b) cheating your way to a win, silently daring your parens to admit you have to have cheated in front of the Quaesitors.
No need to explain this to the player, of course, if you want the full Tytalus experience.
The alternative test for any Tytalus is to kill the master, so...
Create a dead copy of yourself with sun duration and leave your apprentice to find it. By the time they get anyone else to act as witness it should be gone. Conditions of passing are up to the master, obviously...
So the treasure hunt as I originally presented, while an exercise in creativity and tactical challenges, is not exactly a Tytalus challenge.
I may have to rewrite for a Flambeau or Ex Miscellanea. Though what sort of Ex Miscellanea?
PS looking for an NPC apprentice gauntlet that the travelling PCs can interrupt and have the apprentice treat them as a course hazard to deal with/remove
If you are curious I have run this as the gauntlet for two magi with slight variations:
First time was for a Bonisagus with a Co focus , the second time was for a Flambeau (CrIgCo), just rewirked things so that the specimens to hunt were made by another magus in the Covenant and that the Flambeau Mater was setting the hunt as a challenge.