Phi Brain is all about solving puzzles, however if you think that you'll be able to solve puzzles along with the protagonists, then I'll put that hope to rest now; you're not. Whilst you'll get the occasional glimpse at the whole puzzle, they are for the most part exclusively for the characters.
The character designs are very brash and crude, very much like the show itself, and whilst I am hesitant to call them outright bad they are certainly below average. This is a low budget anime, and so the animation and art is poor, expect to see many off model shots every episode, which are often so bad that they are distracting. Whilst this is the case, the animation level doesn't detract too much from the anime as a whole.
The music is worlds apart from the art, the opening "Brain Diver" is a catchy and energetic song that fits the series well, and the ending, "Hologram" is a pleasant track that grows on you as the series progresses. The soundtrack is also pretty good, which at points makes up for the appalling animation quality. It isn't amazing, but is remarkable considering the budget, and works well to make the action scenes tense.
During the first few episodes you will find yourself hard pressed to like the main characters, as the first few episodes focus on making Kaito look as cool as possible by having him casually solve difficult puzzles and the like, to the point where it feels like they're trying to force it down our throats. Gammon comes across as loud and obnoxious, and Cubic seems like an arrogant child prodigy. However as the series progresses past the first few episodes and onto the main plot, the characters become much more likable. This is because they stop trying to outdo each other in both arrogance and in puzzle solving and start working together against the antagonists of the series, the POG.
The story starts off very simply, the POG will set Kaito a puzzle and he'll proceed to solve it using his Orpheus armband, often with the help of one of the geniuses that Kaito meets during the first few episodes. Fortunately the plot becomes more engrossing before too long which makes the series more interesting and reduces the repetitiveness. Don't expect anything deep or complicated from the main plot of Phi Brain as it's still straightforward and standard shounen, but it's an improvement. The puzzles act as a way for the characters to fight each other, and in later episodes "battle puzzles" are introduced, where the two contestants directly match their wits. This is quite entertaining at times, however, the fact you can't see the puzzle in its entirety is frustrating, as it alienates you from the tactics employed.
Phi Brain improves as it progresses, but it never reaches the level of quality I would have liked, however that does not mean it's bereft of entertainment, and although it doesn't have the gripping battles of wit it was aiming for, it's a simple shounen that you can find fairly enjoyable if you aren't feeling too critical.