Anna and Brian are sharing a meal at a restuarant and they agree to split the bill equally. Brian wants to order something that Anna is allergic to though, and they agree that Anna won’t pay for that item. Brian gets the check and calculates Anna’s portion. You must determine if his calculation is correct.

For example, assume the bill has the following prices: bill = [2, 4, 6]. Anna declines to eat item k = bill[2] which costs 6. If Brian calculates the bill correctly, Anna will pay (2 + 4) / 2 = 3. If he includes the cost of bill[2], he will calculate (2 + 4 + 6) / 2 = 6. In the second case, he should refund 3 to Anna.

Marie invented a Time Machine and wants to test it by time-traveling to visit Russia on the Day of the Programmer (the day of the year) during a year in the inclusive range from 1700 to 2700.

From 1700 to 1917, Russia’s official calendar was the Julian calendar; since 1919 they used the Gregorian calendar system. The transition from the Julian to Gregorian calendar system occurred in 1918, when the next day after January was February . This means that in 1918, February was the day of the year in Russia.

In both calendar systems, February is the only month with a variable amount of days; it has 29 days during a leap year, and 28days during all other years. In the Julian calendar, leap years are divisible by 4; in the Gregorian calendar, leap years are either of the following:

You have been asked to help study the population of birds migrating across the continent. Each type of bird you are interested in will be identified by an integer value. Each time a particular kind of bird is spotted, its id number will be added to your array of sightings.

You would like to be able to find out which type of bird is most common given a list of sightings. Your task is to print the type number of that bird and if two or more types of birds are equally common, choose the type with the smallest ID number.

For example, assume your bird sightings are of types ar = [1, 1, 2, 2, 3]. There are two each of types 1 and 2, and one sighting of type 3. Pick the lower of the two types seen twice: type 1.

You are given an array of n integers, ar = [ar[0], ar[1], ..., ar[n - 1], and a positive integer, k. Find and print the number of (i, j) pairs where i < j and ar[i] + ar[j] is divisible by k.

For example, ar = [1, 2, 3, 4, 5, 6] and k = 5. Our three pairs meeting the criteria are [1, 4], [2, 3] and [4, 6].

Lily has a chocolate bar that she wants to share it with Ron for his birthday. Each of the squares has an integer on it. She decides to share a contiguous segment of the bar selected such that the length of the segment matches Ron’s birth month and the sum of the integers on the squares is equal to his birth day. You must determine how many ways she can divide the chocolate.

Consider the chocolate bar as an array of squares, s = [2, 3, 1, 3, 2]. She wants to find segments summing to Ron’s birth day, d = 4 with a length equalling his birth month, m = 2. In this case, there are two segments meeting her criteria: [2, 2] and [1, 3].