Find the smallest positive integer B so that when we express the decimal number 301 as a base B number, we still get a 2-digit number.
For a number to be 2-digits in a certain base, the cub of the base must be more than the number. We can test out all numbeers until one works.
2^3 = 8 < 301
3^3 = 27 < 301
4^3 = 64 < 301
5^3 = 125 < 301
6^3 = 216 < 301
7^3 = 343 > 301
This means that 7 is the smallest value for B that works.