If we want to use bit strings of length at most n to encode not only all 26 letters of the alphabet, but also all 10 decimal digits, what is the smallest number n that works?

Since the question asks for bit strings of length at most n (as opposed to exactly n), we can use bit strings ranging from 1 to n. That is, we want the smallest n that satisfies the inequality (we exclude the 0-length string):

\[2^1 + 2^2 + 2^3 + ... + 2^n >= 36\]

The left hand side sum of the powers of two is equal to \(2^{n+1} - 2\). Solving for n we get:

\[\lceil log_2 38 \rceil - 1 = 5\]

If the question was to find bit strings of exactly length n, then the result would be:

\[\lceil log_2 36 \rceil = 6\]

What is n for Morse code?

Wikipedia chart shows 5, as calculated above