Cube problem

[tytyros]

17 yellow cubes and 10 blue cubes of equal sizes are fastened together to form one large cube as shown in fig.

( refer to the third cube from the top )
http://www.bbc.co.uk/schools/ks3bite...mages/ton2.gif

what is the largest fractional part of surface area of the large cube that could be blue ?

[krovvidy]

For the maximum utilization, let blue cubes are put on the surface ...

Say, 8 corners of the larger cube are the blue cubes (i.e., 3 smaller surfaces are utilized) and the rest of the 2 are on the edges (i.e., 2 smaller surfaces are utilized)

8*3 + 2*2 = 28 smaller blue surfaces

totally there are 6*9 = 54 smaller surfaces ...

Hence the largest fraction part of the surface area of the large cube that could be blue = 28/54 = 14/27