My youngest puppy has excellent problem solving abilities, she thinks entirely too much about the best way to do something "fun" without getting into trouble. It's like she's constantly thinking "Wow, guess I can't launch myself AT you, you don't like that. How about I just jump straight up into the air without making contact? Oh, you don't like that either. How about high speed circles around you? STILL no? Well then I'll go body slam the big dogs, they don't mind".
My shepherds do Math when playing fetch. If they think another dog will get to the ball first, they immediately stop running for it and wait for the other dog to go past them, and then steal it. Logan calculates speed and location and all of it. He knows where he needs to be to get there first and runs full out to ensure a victory. But you can see him think on it quickly and decide. Once he's committed, you better get out of his way. LOL
And they put thought into training ME. Baby pool is empty, let's drag it around the yard until she fills it. They know how to communicate with me just fine. Balls, biscuits, attention, baby pool, they have it down to an art.
The faces my girl Shepherd makes at me, good lord, she's expressive.