Here's how you can incorporate problem solving into game design and mechanics.

This is one way to add problem solving to your game mechanics, add puzzles or challenges to advance in the game. Maybe you have to collect something by solving one puzzle and use that to open a door or drawer, maybe solving a mechanism will open the way or give a hint about the story. Since it will go off track, it will help change the exploring of the game and help improve the player's experience.

To incorporate problem-solving into game design and mechanics, focus on puzzle integration. Start by designing puzzles that naturally fit within the game's narrative and environment, ensuring they enhance rather than disrupt the player's immersion. Use puzzles to challenge players' critical thinking and creativity, progressively increasing their complexity to maintain engagement. Ensure that each puzzle has clear objectives and intuitive mechanics, providing hints or tools to assist players without giving away the solution.

Challenges should adapt to player actions, offering scenarios that require critical thinking and strategic decision-making. For instance, implement enemies with evolving tactics or environments that change based on player choices. Design levels that require creativity, such as manipulating the environment or combining different mechanics. Integrating dynamic challenges creates an immersive, intellectually stimulating experience, encouraging players to think on their feet and adapt their strategies continuously.

Gratification is one the strongest ways to incorporate problem solving in games, and in real life. Allow your players the chance to be rewarded for their efforts, as this will create a simple loop where the player does somethin difficult relative to the game and gets rewarded for it. This loop solidifies an expectation within the player, "If I solve this problem, I'll get rewarded". Your rewards should be leveled against the difficulty of the problem, this not touches the realms of game balance.

Especially in cases where the game is co-op, player collaboration is a unique asset to vary gameplay. If you have no features encouraging collaboration, it a single player played by multiple people, not a multiplayer game. One example of this is in the difference between portal 1 and portal 2. The multiplayer aspect of portal 2 allows it to have an entire new range of puzzles for the players to problem solve, and therefore is distinguished as far more than a clone of its predecessors. It is crucial that, in order to stand out, you must play to your strengths. And as a game allowing for teamwork, you must vary your gameplay to highlight and encourage problem solving with others.

Using an efficient feedback look teaches your player HOW they should solve the problems you offer them to solve. At the beginning of a game the player is given tools, an effective feedback loop allows the player to use them to solve given problems as each system of the game will feed into another cyclically.

Incorporate problem solving into game design and mechanics by creating challenges that require players to think critically and strategize. Design puzzles, quests, and missions that involve logic, pattern recognition, and resource management. Provide players with tools and abilities that can be combined in creative ways to overcome obstacles. Encourage exploration and experimentation within the game world to find solutions. Implement a gradual difficulty curve to ensure players are continually challenged but not frustrated. Use feedback systems to guide players and reward successful problem-solving, enhancing engagement and satisfaction.

Consider yourself from the POV of the player instead of as the Developer, this will give you a perspective that will allow you to think about the dynamics and feelings you want to elicit from players, from there its a matter of designing the multiple elements that could create said dynamics For problem solving these elements range from tools available to player, the environment, the games' other characters, resource management. How you combine and represent your elements will affect the dynamic you want to elicit from your player when they are solving your problems