If you liked the Phi Brain: Kami no Puzzle anime, the Anime-Planet community thinks you'd like:
Some years into the future, a strange, unexplainable natural disaster has broken off a piece of the Japanese mainland. Known as the Lost Ground, it is now inhabited by people with Alters -- machine-like extensions of their own will. In order to keep the peace on the Lost Ground, the HOLY organization uses its own Alter capabilists to police the region. In the midst of the chaos is a young man named Kazuma, whose life will soon change forever as he discovers his hidden abilities, and how to wield them.
This may seem like an odd recommendation, but hear me out - in my opinion, some of the best recommendations out there aren't based solely on plot, but on the relationship between the main characters. For example, Gungrave and Berserk couldn't be less similar when based on story alone, but the char development and char dynamic is dead-on. The same can be said for these two - Kaito and Gammon's comical and at times serious frenemy relationship in Phi Brain is nearly identical to Ryuto and Kazuma in Scryed. If you enjoyed the dynamic in one, try out the other.
Both shows have characters that love to hate each other and plenty of interesting battles occur because of this. Scryed is a little more action adventure based where Phi Brain goes the puzzle solving school life route but either way I'm sure fans of one would enjoy the other.
Ever since Yugi Mutou completed the Millennium Puzzle his life has changed; he's made friends, learned how to play the card game Duel Monsters and has gained more confidence in himself. After his grandfather is beaten in a duel he is challenged by Seto Kaiba, ranked number two in the world, but Yugi beats him regardless. Now, as a result of his victory, Yugi has attracted the attention of the game's creator, Pegasus. Yugi is then challenged to a dual in an alternate reality where magic brings the monsters to life, but is beaten and his grandfather's soul is taken. In order to retrieve it Yugi must now participate in a tournament against the best duelists in the world, defeat the game's creator, and learn more about the secrets within his Millennium Puzzle!
Both of these shows has a type of game where they challenge one another. One has a virtual card game and the other has a variety of life size puzzles. There is a punishment for losing during special games. The main characters even have items that make them better at the game. They repeat the game almost every episode. There is also a villian at points trying to ruin the game or destory the world.
Both of these anime, at their basis, feature some ordinary plaything brought on to a large scale competition with dangerous consequences. Both series can jump back and forth from serious to humorous with thair colorful casts of characters. And of course, the main character is a natural genius at whatever it is the series focuses on.
The mystery of "The Blade Children" is a secret which has remained well-hidden, and has cost some their lives. After Narumi Ayumu's brother disappears in a search for the answer, Narumi is forced to unravel this mystery for himself. Join him in his investigation which will lead him to the secrets of the Blade Children, and to tests of skill which may prove to be fatal.
Spiral feels a lot less shounen and is a lot more serious than Phi Brain - but both involve special 'children' and a whole mess of deadly puzzles, with plenty of analytical thinking and baddies to boot.