I'm a linguist in real life, so memorizing the 10 or so patterns the Enigma Puzzle uses is pretty easy. For the whole team it takes maybe 15 or 20 minutes. Thankfully, you're phased while you do the quest, so no pvp shenanigans as you do it... as compared to the key race :/

So I've now done three ley race dailies on 20 characters without getting group credit once. I talked to the npc, went through all the dialogue, and stood literally on top of her each time. No dice. Sigh.