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 ?

Hi,

We need to find the cubes that are not painted but which are cut. We know that only surface cubes will be painted. So, the cubes which are not painted will be 5^3 = 125. So, imagine a cube made up of only these 125 smaller cubes. Now, when cut diagonally, the cubes that will be cut in each layer will be 5 and there will be 5 such layers. So, total such cubes will be 25.