To find the smallest positive integer B where 301 expressed in base B is a 2-digit number, we need to find a number smaller than 301 that results in a 2-digit number when expressed in various bases.
Starting with B=2 (binary), we have:
301 in binary is 100101101. Since 100101101 has 9 digits, B=2 is not the answer.
Next, we try B=3 (ternary):
301 in ternary is 10201. Since 10201 has 5 digits, B=3 is the answer.
Therefore, the smallest positive integer B is 3.
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.
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