02_01_03.Rmd

---
title: "Exercise 2.1.3"
---

```{r include=FALSE} 
knitr::opts_chunk$set(options(scipen = 999))
knitr::opts_chunk$set(echo = FALSE)
```

> (a) Continuing with Exercise 7 of Chapter 1, compute the maximum number of strings of length at most 3 in a trinary code.

We simply calculate how many strings there are of length 1, 2 and 3 and add the numbers:

$$3^1 + 3^2 + 3^3 = `r n <- 3^1 + 3^2 + 3^3; n`$$

> (b) Repeat for length at most 4.

Similar to (a):

$$3^1 + 3^2 + 3^3 + 3^4 = `r n <- 3^1 + 3^2 + 3^3 + 3^4; n`$$

> (c) Repeat for length exactly 4, but beginning with a 0 or 1.

We have two choices for the first position (0 or 1) and 3 choices for each of the three subsequent positions:

$$2 \cdot 3^3 = `r n <- 2 * 3^3; n`$$