At their best, games can be remarkable platforms for creativity and imaginative problem solving.

Two fine examples — one digital, one analog — of games to make your brain work are Portal 2 and Rory’s Story Cubes.

Portal started as a school project and became one of the most respected designs in recent memory based on the simple genius of its design. The original game wasn’t even published as a stand-alone title: It was bundled as a bonus into a compilation package called The Orange Box (EA/Valve, Windows, Xbox 360, PlayStation 3: $30-$60), along with Half-Life 2 and Team Fortress 2.

Every inch of the original Portal was meticulously crafted, from the levels and puzzles to the outstanding story line and voice acting. Even the song created for the closing credits — Still Alive — became an Internet hit.

Although the game could be finished in about two hours, they were two of the best hours in gaming history.

The premise was loaded with potential. As in most action games, you run around a threatening landscape carrying a gun in a first-person perspective. The gun, however, doesn’t shoot bullets: It shoots portals. The first shot opens an entry portal; the second shot opens an exit portal. You can then walk through the first portal and emerge from the second.

This simple element, when combined with carefully constructed environments, sets up an astonishing array of puzzles. The challenges start simply. If you need to reach a high ledge, you just fire a portal at a nearby wall and then another up by the ledge. As the game proceeds, the environments become more complex. Your portals can be placed to redirect beams to trigger certain actions or allow you to move objects in order to bypass threats or open doors.

Physical modeling plays a huge role, allowing you to place portals in order to build momentum for long jumps. For example, placing one portal on the floor and another directly above it on the ceiling allows you to create a kind of perpetual fall. This builds momentum, which can be converted to energy in order to solve puzzles.

Portal 2 (EA/Valve, Windows: $60; Xbox 360 or PlayStation 3: $60) builds upon all of these elements to create a far more elaborate set of challenges. There is a heavier emphasis on story and humor, with outstanding voice acting matched to terrific comedy writing. It’s a larger, longer game, with fresh ways to interact with the environment.

The new features include “excursion tunnels” to transport objects on a kind of enclosed conveyor belt, “aerial faith plates” that bounce you around a level (they require a “leap of faith” because you’re never quite sure where they’ll leave you), and various gels to boost speed, add bounce or create portal-friendly surfaces.

The designers had a tough act to follow in creating Portal 2, and they accomplished the task with wit, style and imagination. The game is just different enough to make it more interesting and challenging, but the solutions are never overly complex. They require analysis of the environment and the goals and then a logical application of the tools at hand. Parents and kids (tweens and up) can also enjoy this one together, thanks to a cooperative mode that allows two people to play at once.

The game retains an E10 (“Everybody,” ages 10 and up) rating, and there is almost no violent content. However, the tone is consistently dark, and the humor can be a bit crude at times. Some parents may object to passing jokes (made by robots) about adoption and people’s appearances. There is gunfire from robot turrets, and mild swear words are used.

From a complex, high-profile digital entertainment experience, we move to the most fundamental and ancient of gaming elements: dice.

Rory’s Story Cubes (GameWright, $8) were created by Irishman Rory O’Connell as a tool for tapping creativity. The result is not so much a game as it is a “creative story generator.”

There are nine dice in the package, for a total of 54 faces. Each face displays a different icon: apple, fish, lock, rainbow, house, lightning bolt, and so on. Players roll all the dice at once and then choose a starting image. They begin with “Once upon a time” or some similar opening, then use that image to begin a story that will weave together all of the face-up images.

Ten-year-old Meg McDonald rolled turtle, bridge, bee, castle, sad face, cane, magnet, keyhole and plane and had the following story to tell: “There once was a turtle named Bob who lived under a bridge with his friend, a bee. One day, someone built a castle over his bridge, which made Bob very sad. The man who built the castle kept walking over the bridge with his metal cane. This made a horrible clinking noise that kept Bob up all night. One day Bob used his magnet to steal the man’s cane. Without his cane, the man fell over the bridge. Bob rescued him and took him to the castle, but the castle door was locked. Bob asked the bee to climb through the keyhole to open the door. Inside, the man regained consciousness, thanked Bob, and gave him a free plane ticket to Miami as a reward.”

The genius of the design is its simplicity and flexibility. People can collaborate on stories, select themes or just play alone.

Both kids and adults — solo, with a family or even in a party setting — can all enjoy it. Home-schoolers in particular might find it a useful tool for jump-starting the brain before a day of work.

Thomas L. McDonald blogs at StateofPlayBlog.com.