# Missing Morse codes

Morse codes for Latin letters are sequences of between one and four symbols, where each symbol is a dot or a dash. There are 2 possible sequences with one symbol, 4 with two symbols, 8 with three symbols, and 16 with four symbols. This makes a total of 30 sequences with up to four symbols. There are 26 letters, so what are the four missing codes?

Here they are:

```    .-.-
..--
---.
----
```

There are various uses for these codes, such as variants of Latin letters.

The first sequence on the list, `.-.-` is similar to two A’s `.- .-` and is used for variations on A, such as ä or æ.

The sequence `..--` is like a U (`..-`) with an extra dash on the end, and is used for variations on U, like ü.

The sequence `---.` is like O (`---`) with an extra dot on the end, and is used for variations on O, like ö.

The last sequence `----` is used for letters like Ch or Š. Go figure.

## Sequences of length 5

Sequences of five or six symbols are used for numbers, punctuation, and a few miscellaneous tasks, but there are a few unused combinations. (“Unused” is fuzzy here. Maybe some people do or did use these sequences.)

Here are the five-symbol sequences that do not appear in the Wikipedia article on Morse code:

```    ..-.-
.-.--
-..--
-.-.-
-.---
---.-
```

So our of 32 possibilities, people have found uses for 26 of them.

## Sequences of length 6

Out of 64 possible sequences of six symbols, 13 have found a use.

It’s harder to distinguish longer sequences by ear, and so it’s not surprising that most sequences of six symbols are unused; the ones that are used have special patterns that are easier to hear. Here are the ones that are used.

```    ..--..
..--.-
.-..-.
.-.-.-
.--.-.
.----.
-....-
-.-.-.
-.-.--
-.--.-
--..-.
--..--
---...
```