1. The Swedish Cake problem. Difficulty 🌶️🌶️

A cake is left in the common room for everyone to enjoy. People never take more than one piece, but obey the following protocol:

If there is more than 150g then they take a 100g slice.
If there is less than 30g then they take it all.
If there is between 30 and 150g then they take half of the remaining cake.

Write a recursive function to compute the number of people who will get a taste of a cake that weighs x grams. Try to write the type of the function before you start.

2. Weekly sales

This questions is about the weekly sales from a shop, where week numbers start at zero.

Sales i is the sales for week i.
Assume the week number (Int) is positive.
Sales is always non-negative.

import System.Random(randomRs,mkStdGen)

sales :: Int -> Integer
sales i = randomRs (0,1000) (mkStdGen i) !! i
           -- sales in the range 0 - 1000
           -- The definition is not important!

Difficulty 🌶️
Give recursive definitions of functions which compute:

(a) total sales for the first n weeks?
(b) highest sale in the first n weeks?
(c) number of weeks with sales less than 100 in the first n weeks.
(d) Define each of these using list comprehensions instead of recursion

Using recursion, indirectly or in a helper function:

Difficulty 🌶️🌶️
(e) Average sales up to and including week n?

Difficulty 🌶️🌶️🌶️
(f) Give the week numbers of the weeks with the best sales in the first n weeks.
Since there may be more than one week with the best sales, your answer should be a list of weeks.

(g) Write a quickcheck property for (f) which checks that you included all the right weeks in your answer, and none of the wrong ones!