Full question in description box below: (Please help!!)

Question

Morse code is a type of communication that uses lines and dots to represents letters of the alphabet, numbers, and symbols. For example,

-. represents the letter N

-.. represents the letter D

How many letters, numbers, or symbols could be represented with one character?

How many letters, numbers, or symbols could be represented with one or two characters?

How many letters, numbers, or symbols could be represented with one, two, or three characters?

How many characters do you you think are necessary to represent the alphabet and all single digit numbers?

Is this a permutation or combination question? Explain your reasoning.

Answer 1

I'm going to (mis)use the term "alphanumeric character" to cover "letters, numbers, or symbols".

I'll use the term dot-dash to mean either a dot or a dash.

How many alphanumeric characters could be represented with one dot-dash character? 2 (a single dot or a single dash).

How many alphanumerics could be represented with one or two dot-dashes? 2 + 4 (single dot, single dash, dot-dot, dash-dash, dot-dash, and dash-dot).

How many alphanumerics could be represented with one, two, or three dot-dashes? 2 + 4 + 8 (single dot, single dash, dot-dot, dash-dash, dot-dash, dash-dot, dot-dot-dot, dash-dash-dash, ...)

What dot-dash word length do you think is necessary to represent the alphabet and all single digit numbers?

Looks like a dot-dash word length of 5 dot-dashes should do it: that would give 2 + 4 + 8 + 16 + 32 = 62 different possibilities, and there are only 36 alpha + digit values to be represented (assuming that they don't have upper/lower case in Morse code).

Is this a permutation or combination question? I would say permutation, since the the dot-dash sequences definitely have a particular order. dot-dash-dash represents a different alphanumeric character than dash-dot-dash.

Answer 2

So, for this problem you need to consider the fact that you can have - or .

In the case of one character you can either use the - or the . which means that there would only be 2 possibilities.

In the case of two characters, we have to break this into cases:

Case 1: .. In this case, there is only one way to do this

Case 2: -. Here you can make two possibilities (-. or .-)

Case 3: -- Just like in case 1, there is only one way to do this.

Thus, when we have two characters, we have a total of 4 (1 + 2 + 1) possibilities

In the case of three characters, we use cases again:

Case 1: All dots. Here we have only one way to do this

Case 2: 1 dash, 2 dots: Here we would have 3 ways of doing this. (-.., .-., or ..-)

Case 3: 2 dashes, 1 dot: Same as case 2, we have 3 ways

Case 4: 3 dashes: Same as case 1, we have one way

Thus, we have a total of 8 possibilities.

As for the next part, I'll let you kinda think through that one yourself. So far we have 2 + 4 + 8 = 14 characters that we can currently make. The alphabet has 26 letters and there are 10 numbers (0 - 9). Hence you would need a grand total of 36. So the question is, if we had four characters, would this cover the remaining 22 characters? Or do you need to go to five characters? Check the cases.

As for the last question, since we are counting things like .. or -- as one thing this is a combination problem. If this were a permutation problem then .. would be counted as 2 (since 2*1) However, since you read .. the same way regardless of the order, we count this as 2C2 (which is (2*1)/(2*1) = 1)

Hope this helps

Mr. K