Marrying Muffy is, as you'd expect, somewhat similar to marrying Celia, you have to get her to 4 red hearts and then give her a blue feather. Much like Celia runs, I've used a point based system, to determine, how many red hearts Muffy will have. 1 red heart = 1 point 2 red hearts = 7/8 points 3 red hearts = 12 points 4 red hearts = 15/16 points
The big difference between Celia and Muffy, is that for both 2 hearts and 4 hearts, the amount of points required is somewhat random, with 2 hearts either being 7 or 8 points, and 4 hearts being 15 or 16 points. 2 hearts isn't usually a problem, as you have to pass that amount anyway, but 4 hearts can cause a few problems, especially if you try and propose early for a better time.
There are 5 different ways to increase your points with Muffy (6, but doing one of them, means you can't do another) Giving her a flower = 0.5/1 point Giving her milk = 0.5 point Talking to her = 1 point Coin/Moon Ore = 1 point Heart event = 1 point
The reason why Muffy has more ways to increase points than Celia, is because you can give Muffy multiple gifts in one day. However, increasing points using these methods, isn't fully straight forward. When giving Muffy a flower, she'll ask you if the flower is for her, and you'll get three options, Yes, If you want it, and No. Saying no is obviously incorrect, saying if you want it gives you half a point, and saying yes gives you 1 point, but be careful, because the default option is if you want it, and hitting that can cost a bit of time. In terms of how many flowers you should pick up, pick up 3 flowers at the beginning of the run, and then on day 3, after you've talked to her, pick up 6. Giving her milk, is straight forward. Milk your cow on day 1 (before you've talked to her), 2, 3 (depending on whether the ruins are open) and maybe 4 (if you have time) Talking to Muffy, to increase your points, isn't just talking to her. After you've talked to a few times, she'll ask why you're here, and to get the point you need to respond with, to see you, which for the first half of the run, is the default option. However, after 3 hearts, the answers all switch round, and the "to see you" answer is the second option. It's also worth mentioning, that you cannot get this point, when Muffy is outside of the bar, it only works when she is inside the bar but not working.
In order to explain the next section, I'm going to first explain a strange part of the run. As you may know, Muffy works in the Blue Bar, which is open from 10:00am, until when, I don't know. Muffy starts her shift around 1:00pm-ish, with the exception of Spring 3 when you get the first heart event. When Muffy is working, she won't accept any gifts from you. Considering she works until very late, there's no point in trying to catch her at the end of her shift, but instead, you need to come back at 10:00am the next day, which means waiting around 3 minutes. But this doesn't mean those 3 minutes have to be wasted, as they can be spent in the ruins, trying to dig up coins and moon ores, to give to Muffy. The major problem with this, is that it's reliant on RNG. You don't know whether you'll get any coins or moon ores, but the more the better. Sometimes Carter won't even be in the ruins, and you can't dig at all. If this happens, then a good back up strat is to feed and milk your cow, and then milk your cow again, the next day. If you do this, you should be able to sell your cow straight after you milk it. If you do manage to get any coins or moon ores, then you can give one a day to Muffy, with all the other gifts.
There are 2 heart events you can activate during a run, but sometimes there's 3, if you're a bit behind on points.
Heart Event Guide:
The first heart event happens on Spring 3, at around 1:00pm-ish, but can happen on Spring 2. All you have to do is leave your house normally, and the event should start. Even though this event has two option boxes, the correct answers are the default ones, for both of them. The second one is a bit more random about when it happens, but it's usually around Spring 6, afternoon-ish. To activate this event, all you need to do is enter the Blue Bar. This is another event where you can just mash A because the correct option is the default one. There is a third event, which can sometimes come up, around the beginning of Summer. I'm not entirely sure, but I think this event triggers, if you either aren't on 3 hearts, or aren't close to 4. The event activates upon leaving your house. Because this event is more likely to trigger in run that goes further into summer than necessary, it's quite crucial that you correctly answer it's one option box, with the second option. This has only happened to me once, but there's also a possible fourth event, which happens around 6:30pm-ish, once you have 4 hearts (I think). The only way this event should activate, is if you're not able to visit Muffy in the afternoon of the next day, because she'll be working. If you do activate this event, just mash through it, to get through it safely, because if you're not sure on how many points/hearts you have, this can still boost you up.
That's pretty much it for Muffy For a guide that lists all/most big and small time saves for this category, that I can think of, read this ---> http://pastebin.com/jCbvKbei