__Problem of the Week__

__9/18/17__

__Painted Cube__

A cube has an edge length of 4
in. The cube is painted red all over and then cut into 64 cubes of edge length
1 in. How many of these cubes have exactly one face painted red?

__9/11/17__

__No Fives__

How many six-digit whole numbers are there which DO
NOT contain a 5?

__Solution__

Let the six digits number be abcdef, which a,
b, c, d ,e, f represent a digit respectively.

For a, neither 0 nor 5 could place in it,
thus, 8 digits are available here (1,2,3,4,6,7,8,9)

For b, c, d, e and f, they can't contain 5,
hence, 9 digits are available for them (0,1,2,3,4,6,7,8,9)

Therefore, the number of six digits number
which does not contain any 5 is

8 * 9 * 9 * 9 * 9
*9 = 472,392 .

##