## 14 Apr PMCA Saturday 18:30 Python Homework 22.04.09.

**Question 1:**

The *hailstone sequence* starting at a positive integer `n`

is generated by following two simple rules. If `n`

is even, the next number in the sequence is `n/2`

. If `n`

is odd, the next number in the sequence is `3*n+1`

. Repeating this process, we generate the hailstone sequence. Write a recursive function `hailstone(n)`

which prints the hailstone sequence beginning at `n`

. Stop when the sequence reaches the number `1`

(since otherwise, we would loop forever 1, 4, 2, 1, 4, 2, …)

For example, when `n=5`

, your program should output the following sequence:

5 16 8 4 2 1

**Question 2:**

Use recursion to write a function `multisplit`

that consumes two positive integers `total`

and `split`

and produces the number of times `total`

is repeatedly divided into `split`

even pieces before each piece is of size at most 1.

For example, the value returned by `multisplit(8, 2)`

will be 3, since 8 can be split into 2 pieces of size 4, which are then each split into 2 pieces of size 2, which are then each split into 2 pieces of size 1 (at which point no further splitting takes place since the pieces are of size at most 1). The value returned by `multisplit(8, 3)`

will be 2, since 8 can be split into 3 pieces of size 8/3, which are then each split into 3 pieces of size 8/9 (at which point no further splitting takes place since the pieces are of size at most 1).

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