SOLUTION: How many different signals consisting of five symbols or less can be sent using the dot and dash of Morse code?

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Question 1191625: How many different signals consisting of five symbols or less can be sent using the dot and dash of Morse code?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How many different signals consisting of five symbols or less can be sent using the dot and dash of Morse code?
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Each position is 1 of 2.
---> 1 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 = 63
E is one dot.
T is one dash.
I didn't include an "empty signal." 2^0 is 1. It's the code for and E or a T.
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There are 26 Morse codes for A-Z, 10 for 0 to 9 that use 5 or fewer dots/dashes.
Some others, eg, the period and the comma, use 6.
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You never outgrow your need for useless facts.
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I'll list them. I'll use 1 for dash and 0 for dot.
1  0
2  1
3  10
4  11
5  100
6  101
7  110
8  111
9  1001
10 1010
11 1011
12 1100
13 1011
14 1100
15 1101
16 1101
17 1110
18 1111
19 10000
20 10001
BBL to finish.
21 LSLS
22 LSSS
23 SLLL
24 SLLS
25 SLSL
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many different signals consisting of five symbols or less can be sent
using the dot and dash of Morse code?
~~~~~~~~~~~~~~~~ 

The number of different signals using precisely n symbols 
(dot or dash of Morse code) is  2%5En,  n= 1, 2, 4, . . . 


Therefore, the answer to the problem's question is


    N(signals) = 2%5E1 + 2%5E2 + 2%5E3 + 2%5E4 + 2%5E5 = 2 + 4 + 8 + 16 + 32 = 62.    ANSWER

Solved.


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The  " 1 "  in the formula by  Alan corresponds to the empty word  (= empty signal)

            despite Alan's statement that he does not use empty signal.


I do not consider the empty word  (empty signal)  as a real signal and do not count it;

therefore,  my answer is one unit less than the answer given by Alan.