Let's admit it now. Problem-solving with very young children doesn't always work. Like at the end of the birthday party, or the beginning of a head cold. Or both.
Teaching kids to solve problems on their own doesn't have to be hard. And it has tons of advantages in the long run. But it does include a lot of restraint on the part of the average parent. Try doing it the way childcare teachers do. Resist the urge to run to their rescue. Take your time. This holds nothing but advantages for both parent and child unless they're in real physical danger (or fighting and yelling). It also helps your kids learn to be more patient.
I talked a lot about non-violent communication in lesson 3. If you haven't read that yet, you might want to take a look. Here's my condensed version of problem-solving 101 for tired and frustrated parents. When a child asks you for help and you wish they’d try and figure it out themselves, instead of saying no or dropping what you're doing to run and help, say this:
OK, I'll help you with that puzzle (or that shoe) as soon as I'm done emptying the dishwasher (or changing baby's diaper) or whatever. It should take me about 5 minutes and then I’ll be there. Ignore any whining and follow through with what you said you'd do, no more and no less. This works because kids feel supported and you stay assertive. You claim your own feelings by saying, "I need time", using an "I" message to your best advantage. Your kids may figure it before you get over to help. Then you both win! Because I care for so many small children all at once, I’m pretty much always busy but if not, I improvise. There's a book display that always needs re-arranging and I'm not afraid to take the time to do it. That is if and when I feel the child may be better off without my help in this particular instance.