Question

Find the smallest positive integer B so that when we express the decimal number 99 as a base B number, we still get a 2-digit number.

Answer 1

To express the decimal number 99 as a base B number, we need to find the largest power of B that is less than 99. In this case, we want the base B number to be a 2-digit number.

Let's start with B = 2:
99 in base 2 is 1100011, which is a 7-digit number.

Next, try B = 3:
99 in base 3 is 10200, which is a 5-digit number.

Then, try B = 4:
99 in base 4 is 1323, which is a 4-digit number.

Therefore, the smallest positive integer B so that when we express the decimal number 99 as a base B number, we still get a 2-digit number is B = 5.