September 23, 2018

## Exercism - Collatz Conjecture

There are lots of different ways to approach every exercise on Exercism. Why not see how others have solved it?

### Instructions

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.

Examples

Starting with n = 12, the steps would be as follows:

12

6

3

10

5

16

8

4

2

1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

### Solution

Basically using `arity`

and `recursion`

functionalities.

```
(ns collatz-conjecture)
(defn collatz
([n] (collatz n 0))
([n step]
(if (= n 1)
step
(if (even? n)
(collatz (/ n 2) (+ step 1))
(collatz (+ 1 (* n 3)) (+ step 1))))))
```

**Link to solution at Exercism**: Link