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Problem of the Week

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?

No Fives


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


Show Your Work!


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 numbers which do not contain any 5 is

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