Question

What is the sum of all positive integers that have twice as many digits when written in base $2$ as they have when written in base $3$? Express your answer in base $10$.

Answer 1

Only two positive integers, 2 and 8, fit the description.

2 = 10 (base 2) = 2 (base 3)

8 = 1000 (base 2) = 22 (base 3)

Their sum is 10.