Hey everyone! I'm a new DM and about to start Lost Mines for a group of 5. 2 experienced players and 3 newbies. I want to add/tweak LMoP. 

Specifically, I want to add a larger story to continue the campaign after LMoP in which there's an apprentice wizard gone rogue and is causing mayhem throughout the Sword Coast. I will eventually do puzzles/traps based on elements and just magic in general.  I want the party to encounter a time loop puzzle in Wave Echo Cave but I'm struggling to figure it out. I got the idea from Buffy in which she needs to satisfy a customers needs to end the time loop. 

My only ideas thus far have been to have a cursed object in which the wizard was practicing time manipulation and the item Just sends them back to the beginning of this section of the dungeon. They can't destroy the item as it would just send them back to the entrance of this section of the dungeon. Maybe have the markings of time on the floor and they need to use the item in a certain way or place it somewhere. My creative juices just aren't flowing but I just absolutely love this idea. 

Any ideas? Have any of you ever done time loop stuff before?

The best advice I can give re: puzzle creation is allow for more than one solution. What if your party never figures out how to use that amulet in the correct way? Be open to other ideas. If the players suggest something that sounds reasonable, go with it.

I did a similar puzzle once. A sleeping hill giant was guarding a passage in a forest. The players had to get past him to proceed, and to get past him they needed to wake him and tell him his name. If they tried to sneak past, or take a different route, they would eventually be deposited back into the same clearing with the same sleeping giant blocking the same passage, so kind of a time/space loop. In this case, I actually didn't write a solution at all. Maybe they could use magic to get him to reveal his name, or maybe a character with proficiency in history could intuit the name based on local giant lore, etc. In the past I would always come up with a solution or two, but this time I decided to totally trust my players to come up with something that made sense. And they did! The rogue managed to roll some incredible stealth and investigation rolls and discovered that his name was written on the inside of his loin cloth. I hadn't seen that one coming, hadn't considered it as a solution, but everyone was jazzed about it and the rolls were high so I went with it. I was really proud of them for that one.

If you create a puzzle with only one solution, you risk the players not finding it, becoming frustrated, and, worst of all, not having any fun. The only other thing I can think of is give plenty of clues and opportunities for them to be able to figure it out. Use foreshadowing--this is actually my favorite method, because in my experience players love it when something they learned earlier pays off in a later encounter. You don't have to spell it out to them, but they don't need to be particularly subtle either. This article from DM David about puzzle traps may be helpful in that regard. 

Hope this was helpful, and happy DMing!

Perhaps you can locate the puzzle in the spell forge room, and involving the creature that resides there. That place seems exactly where such a bizarre magical phenomenon might form. Perhaps the creature wants to believe everything is fine and when it gets confused and worried by anything there is a break in reality and things go back to before they entered the room. When the characters arrive back in there the creature has no memory of them. The PCs might need to fulfil 3 or 4 out of 12 possible things you could imagine should be improved before the creature is satisfied, plus they can deceive their asses off. Disguises, kill the monsters, light the smelter, carry tools, use the forge, ask the wraith for the secret password of the wizards, yadda yadda, or get annoyed and try to murder your way out of the situation. Insight, Arcana and Investigation checks could reveal clues for possible solutions.

I think I may have responded to your question in another forum, but I couldn't post a link, so I'll reply here too.  :)

I've done something similar to this. I created a room of "Deja Vu", the party enters a room that looks like a fantastic place to rest. However, they can look out and see themselves from about 5 minutes ago, in the past. If their past catches up with them, time loops back to when they first entered the room. This loop repeats over and over until they leave the room. Once they leave the room, they suffer the effects of Deja Vu and are forced to repeat actions for a certain period of time.

I did an entire puzzle video on this idea and its on my YouTube Channel if you want to take a look. D&D 5E Puzzle - Deja Vu

Sounds like a fun idea you have cooked up there! Good luck!