In Morse code, symbols are represented by variable length sequences of dots and dashes. (For example, A = · −, 1 = · − − − −, and ? = · · − − · ·.) How many different symbols can be represented by sequences of seven or fewer dots and dashes?
I don't have a answer for this question but my solution is: $2^1$ + $2^2$ + $2^3$ + $2^4$ + $2^5$ + $2^6$ +$ 2^7$ $= 254$. Is that correct?
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$\begingroup$Yes, you are right. There are $2^n$ Morse strings of length exactly $n$, and the number of non-empty strings of length at most seven is obtained by summing over strings of length $1$, ..., $7$.
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