Question

What's the largest 3-digit base 14 integer?

Answer 1

Base 10 has the ten digits: {0, 1, 2, 3, 4, 5, 6,7, 8, 9}

Base 11 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A} where A is treated as a single digit number

Base 12 has the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}

Base 13 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C}

Base 14 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D}

The digit D is the largest single digit of that last set. So the largest 3-digit base 14 integer is DDD which is the final answer

Note: It is similar to how 999 is the largest 3-digit base 10 integer