"Can't"

Of course she does! She's only 3. Encourage her to try, show her how to try, and give her some slack for acting her age.

Its her age... but ALSO....
Teaching "problem solving"... is just a matter of teaching a child, that there are MANY DIFFERENT ways of doing things. Not only 1 way... nor just someone else's way.

I always taught/emphasized with my kids, since a young age, just that concept. BUT you also have to 'show' them... different ways of doing things... that its okay... and how fun it can be to think of something. When they come up with an idea... praise them.

Your daughter is only 3 years old... even many Kindergarten age children, are still learning this.

ALSO watch your "expectations" of her... for some children, the feeling that they are 'expected' to be a certain way or do something a certain way... will just lead them to feel, like they 'can't' do it. Because, they don't want to let their parent down....
So, the best thing, is NOT to have "expectations"... that are exceeding the child's age-stage. Otherwise, they are self-defeated.

Also teach 'creativity'... to her. That also incorporates SELF-reliance and problem-solving... and being self-assured... of expressing... themselves....

All these things, goes hand-in-hand with each other.

But personally and for my kids, I have found, that 'expecting' them to be a certain way or to do things a certain way... can sometimes lead the child to think "I can't...." because... they are very aware... of the expectancy upon them... versus being themselves....

You don't need games to teach them problem-solving. Just show them with everyday daily things in life. If their toy drops... and they tell you "Mommy my toy dropped and rolled.. under the sofa... can you get it?" Say to her "Oh yes it did sweetie... hmm... I wonder how you can get it? What do you think???" Then, on the floor, with her.... ask her if she can reach it with her arms and hands? If not, then say "Hmm... its too far under the sofa to reach... what can we try???" Then you might say "Hmmm... hey I bet it we use a broom stick or hanger to reach under there... we might be able to reach for it. Shall we try?" Then, get a broom handle... and then SHOW her 'how'... using the broom-stick... to stick it under the sofa... to 'reach' for her toy. And then you do it, to show her. THEN... put the toy back under the sofa... and let her try it Herself.... "guiding" her along the way... and 'how' to use a 'tool' to reach under the sofa to get her toy.....
That is how I teach my kids... and what I have actually done, with my kids since they were 2 years old. So well as they got older, now if something rolls under the sofa... they CAN get it themselves... they go and get a broomstick... or something long... and reach for it under the sofa themselves. BRAVO! They can problem solve!
Just one example.

Just teach your daughter, in everyday life, alternate ways of doing things. Its not about what is 'right' or 'wrong'.... but that ANYONE can think of different ways... to problem-solve... and thereby... they feel more "confident" and self-assured... and self-reliant....

all the best,
Susan

What is she saying "I can't" do? My son was lazy and if he didn't like doing something he would give the "I can't" response. We always were very firm with him that if he didn't try no one was going to do it for him. If he tried and failed we would help. My daughter is afraid of failure so that is her reason for "I can't" so we always make a point to remind her of all of the great mistakes that changed the world. (The microwave is a great example because it is something we use a lot) Once you identify why she is doing this you can easily fix it by modifying how you approach the situation. If her confidence is lacking maybe saying you are going to help without actually doing it will work. Like if she says she can't get herself dressed you could say ok let me help you. You put on your shirt while I get your pants out. Once she gets the shirt on offer to get out her socks, then shoes, by the time she gets her socks on you can offer to get her hair ribbons or coat ready. Then once she is completely dressed point out to her with great fanfare that SHE did it by herself. It will help her confidence and she will soon learn she doesn't need you there all the time. Good luck!

My daughter used to do this around this age. If you have a younger sibling in the picture that could be part of it. My daughter used to tell me that she "couldn't" do things that she was easily able to do, like get dressed. Because I had to still dress her brother (because he was younger and truly couldn't, she had a perception that her was getting more attention. I expected her to dress herself because she is older and able to do it.) So what I started doing was saying, " I know that you can get dressed all by yourself. I help brother get dressed because he's too little to do it himself. Do you WANT Mommy to help you get dressed this time?" Just giving that little bit of extra and teaching her to say what she really meant made a huge difference. It will also help her later if you label and validate her feelings with her. " You seem frustrated that you can't button that button." "Are you jealous that I have to change brother's diaper now and I can't read with you? We can read together as soon as I'm done."

Good luck!