Dogs are naturally pack animals and as such they are constantly interacting with other members of their species. This includes playing games with each other as well as understanding and working within the hierarchy of the pack. Even in the most domesticated breeds that have always lived as single pets in a human household, the ability to work within the pack, which is now the human family, makes the dog a true companion pet for the humans in the home.
However, living as a single dog in a household also means that there is limited interaction with other dogs and often also with the humans in the family. After all people have to go to work, school and outside of the home to places where dogs simply can't go. This means that dogs are left alone, often for a significant amount of time on a daily basis. This relative isolation can cause some dogs, especially those that are the "thinking" breeds, to turn their attention to destructive behaviors that often leads to problems for both the dog and the family.
There are many different breeds and types of dogs that really need routine mental challenges and stimulation to avoid the destructive boredom types of behaviors. Typically the winter months when dogs are more likely to be confined to the house and when cold weather limits their outside time are the most problematic for boredom related problems. Giving your dog some mental challenges and exercise before you leave the home is a great idea, plus there are some options to keep your dog entertained when you are gone as well.
Not surprisingly, training routines and obedience work is a great way to give your dog a combination of mental and physical exercise. If you have a basement or heated garage you may want to consider setting up a training area that includes a few agility types of obstacles that you can work the dog through before you leave them alone. Just be sure all the surfaces are non-slip and that your dog is not going to be at risk of injury should he or she slip or fall. Avoid the high obstacles such as a walk-over or A-frame unless you can provide a lot of mats or carpeted area under the particular obstacle. Outdoors on soft ground this is rarely an issue but on cement or indoor flooring it is a significant factor.
Working a dog through weaving poles, over small jumps or even through a modified tunnel in a variety of combinations can give them something to think about and a mental challenge to complete. You can always throw in some obedience work in the middle of the routine including sit, stay, fetch and some of the more advanced tricks. The more that you change up the routine but also make it fun for the dog the more beneficial this will be. This is also a great way to keep your training engaging for the dog and prevent any boredom with highly repetitive types of activities.
Playing mental challenge games with your dog is a wonderful option and lots of fun for the whole family. For dogs that have scent ability, which is virtually any breed, consider a game of hide and seek with a favorite toy. Start by having the dog sit and stay while you walk away from the dog with the toy. Place it in easy sight of the dog and tell him or her to "find the toy" or whatever command you want to use. Praise them when they bring it back to you or give them a bit of help if they aren't familiar with the game of fetch.
Over time gradually move the toy further away from the dog and start to place it behind objects or under furniture. Always ensure that the dog can find the toy until they are completely sure as to what you are asking them to do. After the dog has a bit of practice with the game you can start hiding the toy in other rooms or in more challenging locations. Be careful hiding it in cupboards and closets as you may teach your dog to go into places that you really don't want them to be.
Puzzle games that provide mental challenges are great for dogs to play with both when you are home and when you are gone. When you are at home playing with the dog with the toy encourages the dog to see the toy as a favorite, making it more likely they will also play with it while you are away. Many puzzle toys have parts that are inside the main toy, with the object of the puzzle for the dog to figure out how to get the smaller toys out of the larger one. These toys need to be appropriately sized for dogs and also durable enough to withstand your dog's chewing.
One great puzzle type of toy is a new variation on the old shell game. A box, often wooden but sometimes durable plastic is covered with sliding covers in long strips down the box. Under the sliding strips are small hollowed out holes into which dog treats can be placed. The slides are then moved to the correct location to cover the holes. The dog is then has to use his or her paws to move the sliders to unveil the treats. Some dogs actually use problem solving techniques of sniffing each slider before deciding which ones to move while other dogs just paw at all the sliders until they find what they want.
Puzzles can also include boxes with levers a dog must pull or push to get a treat or even puzzles where the dog can produce different sounds by pressing on a specific area of the puzzle. Any of these types of activities are great to engage the dog both as a toy and also as a way to stay entertained and mentally stimulated in a positive way.