A cube of dimension 7*7*7 units is formed using 343 unit cubes .All the faces of large cube thus formed are painted blue .If the large cube is cut into 2 symmetrical halves by making a cut along diagonal of one of its faces such that cut passes through two diagonally opposite edges ,how many unit cubes which are not painted on any face will be cut ?

The cut will go through a total of 49 cubes (Imagine a cube with 7 layers of 7*7 cubes, and a cut going along a diagonal of all these layers. Among these 49 cubes, 7 cubes in top and bottom layer would be colored. Also, for the cubes along the edges (7+7) will be colored. Since we have already considered the top and bottom layer edges cube twice we would remove them. So total number of cubes which were colored but were cut= 24(14+14-4). Units cubes which were not painted but cut=49-24=25