One easy method to entertain a bored dog is scattering his food all over the garden (house if there's plenty snow).
Of course it has to be dry food and it works only with a greedy feeder.
I used to do this with my Mäxi. He was so greedy, he would have done three somersaults for the tiniest morsel of dry food, lol. Sometimes I threw out his food in the garden by the handful, so it scattered all over the place.
This is a great idea, only with Charlie it would have to be treats or nuts or bites of meat or cheese. He does not get excited about dry food. I know some dogs immediately scarf down whatever dry food they're given, but Charlie lets his sit and kind of grazes on it when he's in the mood. (It might have something to do with the fact that I usually give him a bite or two of whatever protein food I eat, plus half a treat as a reward when he comes back in from peeing or pooping outside.

)
. Intensive nosework (literally translated, I don't know the technical term in English)
I can't think of anything more specific than sniffing or searching, neither of which packs as much meaning into one word as German does -- as usual!
Mental work is also tiring for dogs.
A dog-loving friend gave me this tip years ago, and I think you're absolutely right. She recommended a toy that you put food inside, and the dog has to figure out how to get it out. Good idea, but I've never seen one.
Try teaching him tricks. Clicker training, dummy training are good methods, but you can of course work according to your own ideas.
Though this sounds kind of labor intensive for me. To be honest, Charlie barely knows "sit" and "come" because I've been too lazy to teach him and because he's smart and amiable enough that he usually gets the gist of what I want and tries to do it, and if he doesn't he's small enough that I can pick him up. But he does know a few commands. He knows "no," and when he's going outside and tries to take a sock with him, I can say "drop the sock" and he immediately does it.
I think he's forgotten the word "walk" because I haven't dared use it around him in years. But don't even think of saying "squirrel" -- or even anything that sounds remotely like that word. I feel too guilty using that word to trick him to go outside, but really all I have to do is look out a back window and gasp or call his name in a hushed, urgent tone.
Used to be, when he got into things he shouldn't I would tell him to drop it and he'd veeerrrry slowly, very reluctantly, very guiltily do so. Then I would give him a treat as a reward. So eventually he came up with an idea -- he'd go find something he knows he shouldn't have (like, say, the cardboard from a toilet-paper roll), then come into my office and ostentatiously start chewing it where I could hear him. I'd tell him to drop it and he'd eagerly do so, awaiting his treat.
It took him a little longer to figure out that trick than it took my son with his sticker chart. Cy learned after a day or two that if he was doing something naughty but stopped when I told him to, he'd get a sticker. This method was based on advice from a therapist. He quickly learned to start doing a naughty thing on purpose, just so he could obey me and get the sticker. Charlie took more like months or maybe even a couple of years to learn the same lesson. But apparently even my dog is smarter than that therapist.
It's also good to have a "start" and "finish" command, so he knows when a session of fun begins/ends. Then you have to be consequent and not throw the socks a single time after saying the finish command, no matter how much he tries to manipulate you into throwing one more time. After a while, he will know and hopefully accept it.
Another excellent idea!
