The Power of Three is the fourth episode of the seventh series of Doctor Who, starring Matt Smith as the Eleventh Doctor, Karen Gillam as Amy Pond, and Arthur Darvill as Rory Williams. It also features Mark Williams as Brian Williams, and introduces Jemma Redgrave as Kate Stewart, the daughter of Brigadier Lethbridge-Stewart, the new commander of UNIT.
The episode's name is either a double or (more fittingly) a triple pun, describing both the fact that there is an invasion of mysterious cubes, that the episode is solved using the team work of the lead trio, and the fact that the entire episode is a homage to the adventures of The Third Doctor.
The episode takes on earth, where a great number of mysterious, yet featureless and seemingly non-threatening little black cubes has taken over the world. The Doctor must spend time on earth with Amy and Rory, trying to deal with the seeming boredom of mundane life, while the mystery of the black cubes runs its course. Or as close as he can manage: there is a bit with Henry VIII and the Zygons. The cubes tend to indeed be another alien invasion, which the Doctor solves through the ingenious method of reversing polarity. Everyone then learns the true meaning of friendship.
In a season that has already seen three big episodes, and which would see even a bigger one, “The Power of Three” is a breather episode, focusing on the characters (and actors) chemistry, as well as providing some comedic scenes and lines. It does have a bit more significance than that, since it also establishes (as some fans had already theorized) that parts of this seventh series were not being shown in the order that they occurred.
I found this episode fun, although compared to some of the more epic and dramatic fare that I had grown accustomed to, it seemed a little overwhelming.