Problem 1:
Write a function largerIndex(c) that takes as input a list c of numbers, and returns a new list k, such that k[i] = 1 if c[i] > i, k[i] = 0 if c[i] = i, k[i] = -1 if c[i] < i.
Test cases:
l1 = [1,2,0,4,2,1,40,-5]
l2 = [0,3,2,1,32,3,4,0]
largerIndex(l1) should return [1, 1, -1, 1, -1, -1, 1, -1]. largerIndex(l2) should return [0, 1, 0, -1, 1, -1, -1, -1].
Problem 2:
Write a function squareUpTo(n) that takes as input a positive integer n, and returns a list of all the square numbers up to (and possibly including) n.
Test cases:
squareUpTo(10) should return [0, 1, 4, 9].
squareUpTo(100) should return [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100].
Problem 3:
Write a function flip1in3() that uses only \fair coins" to generate a \biased coin" with success probability 1=3. That is, this function returns False with probability 2=3 and returns True with probability 1=3.
Problem 4:
Write a function duplicates(c) that takes as input a list c of integers. Some elements appear twice and others appear once. The function outputs all the elements as a list that appear twice in the list c. The elements in the output should preserve the original order.
Test cases:
l3 = [1,2,5,3,6,2,4,5]
l4 = [1,3,5,5,1,4,3] duplicates(l3) should return [2,5]. duplicates(l4) should return [1,3,5].
