The hardest problems to solve are those that are caused by unsolved problems. Thus, sometimes the best way to solve a problem is to address some other problem. Taking the time to find the root of a causal chain can be the difference between treating the cause and treating the symptoms.
Let's say you want to solve the problem of dirty dishes piling up rather than getting washed. What's the solution? To stop being lazy and wash the dishes? That would do it, but if that's your whole solution, you may be doing more work than you need to. Ultimately, washing the dishes will be part of the solution, but there's more to it.
For one thing, loading all the dishes into the dishwasher can take a little time, and generally needs to be done at a time when you feel most like lounging around--right after eating. So how can that task be made easier? By loading dirty dishes into the dishwasher immediately after use, rather than leaving them out till it's time to do a load. Solution found? Problem solved? Not yet.
You can't load dirty dishes into the dishwasher immediately if the clean dishes from the last load are still in it. This is where my family ran into trouble for a long time. The first step to solving the problem was to start unloading the dishwasher immediately after each load. Then it was easier to get the dishwasher loaded, because, by putting dirty dishes into it as soon as we were done with them, the task was spread out more, and less of the work had to be done when we felt least like doing it. Then it was easier to get the dishes washed before they piled up in the sink. Then we got more accustomed to having a clean kitchen, so messiness motivated us to clean it up more. We unlocked the problem chain at its base, gave it a yank, and the rest of the chain followed.
Another example: let's say you have a child whose room is littered with dirty clothes. Sure, the problem is that they never put them in the hamper, but the best solution may not be to bug them to quit being lazy and start putting their clothes in the hamper. A better solution might be to get them their own hamper that they keep in their room, rather than requiring them to make a trip to the laundry room every time they take something off. Of course, some people will still drop their clothes on the floor even if the hamper is three feet away (I've seen this with garbage--people dropping it on the floor even though a waste basket was a few feet away!), but if you don't already have a hamper in your child's room, you may be able to save yourself a lot of grief by getting them one.
A more esoteric example from chess: let's say you want to clear one of your opponent's pawns off of its square, but it has another pawn protecting it. You can capture that first pawn, have whatever piece you captured it with get captured in return, and capture the second pawn. If you do that, you will have succeeded in clearing the square of opposing pawns, but it will have cost you a piece to do it. Sometimes that's the best solution, but when possible, it may be better to start by capturing the pawn that's protecting the one you ultimately want to remove. Then you'll be able clear the square without losing any pieces.
That example may be a little uninteresting for those of you who don't play chess, but it illustrates the point well that solving problems at the root of the chain (in fact, diagonal lines of pawns in chess are called "pawn chains") is often the less costly solution in terms of time, effort, resources, etc.
A more serious example problem: a marriage partner who's considering being unfaithful. Is the solution for them to get control of their thoughts and resist their impulses? Sure, that's part of it. But consider their reasons for looking outside their marriage--apparently they're not finding something they're looking for inside the marriage. Whose fault is that? It may be entirely theirs--they may just be selfish, hedonistic, etc. It may be largely the spouses fault--they may be the selfish one who's not putting anything into the relationship. It may be shared between them both. But that may all be beside the point. Perhaps they've made the mistake of thinking that it's not possible to find fulfillment within their marriage, when in fact they could if some other problems were solved. More on that in a moment.
It can be difficult to step outside of one's present reality and envision what could be. But doing so will often lead to a "cheaper" solution to one's problems. Let's say you've spent years building up a business, and recently, it has started losing money. Do you dump the whole business, and try to start a new one? Maybe sometimes. But usually the better solution is to figure out ways to improve your current business to cut costs or increase revenues.
The same can be true of relationships: rather than looking for someone new, or if you think you've found someone new, rather than destroying your current relationship to make room for the new one, both of which can be "costly" in a variety of ways, maybe the better solution is to rethink your current relationship and figure out ways to improve it. If one person doesn't feel the other is giving enough to the relationship, they might consider whether the other person feels the same way. Pick up some of your partner's chores (and don't do it grudgingly, or thinking that you're paying the price and require something in return), and see whether it makes you feel more involved in the relationship. See if it makes your partner feel like you care about them. Perhaps they'll reciprocate. If not, talk about it with them. Maybe even talk about it with them if they do reciprocate. In fact, definitely talk about the relationship! If you can establish that you both would like to improve your relationship, then you can start working together, rather than fighting against each other to try to get your "fair share". The less you spend fighting each other, the more you have to enjoy together.
Well, I'm drifting off topic, so perhaps it's time to close. Look for the root causes of problems, and you'll find the solutions easier. Don't just sit around until you find an effortless solution, because some problems do require a lot of work, but cultivate greater awareness of related issues and more comprehensive solutions than those you've looked to in the past. You may find magic on the other side of the mobius strip.