Question

If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digit of n3 ?

Answer 1

Answer:

The question is fairly straightforward, it basically asks: which digits can be the units digit of a perfect cube.

Can it be 0? Yes, 10^3=1,000.

Can it be 1? Yes, 1^3=1.

Can it be 2? Yes, 8^3=512.

Can it be 3? Yes, 7^3=343.

Can it be 4? Yes, 4^3=64.

Can it be 5? Yes, 5^3=125.

Can it be 6? Yes, 6^3=...6.

Can it be 7? Yes, 3^3=27.

Can it be 8? Yes, 2^3=8.

Can it be 9? Yes, 9^3=...9.