Gildore

The story begins with the arrival of the "Enemies," giant, indestructible monsters that cannot be negotiated with. The Enemies drive humanity to the brink of extinction. A lone boy stopped them with his "moonfall strategy," but he disappeared soon after. After three years, a boy known as Kyle Kamishiro appears on the outskirts of a city. When monsters attack again, he demonstrates the power to manipulate the odds of probability. Despite his efforts, he is afterward drafted into the "Guilty Children," a unit of children who are guilty of crimes.

(Source: Anime News Network)

Published version of the light novel serialized in Young Magazine the 3rd, "completely rewritten" from the serialized version.