John Watson knows of an operation called a right circular rotation on an array of integers. One rotation operation moves the last array element to the first position and shifts all remaining elements right one. To test Sherlock’s abilities, Watson provides Sherlock with an array of integers. Sherlock is to perform the rotation operation a number of times then determine the value of the element at a given position.

For each array, perform a number of right circular rotations and return the value of the element at a given index.

For example, array a = [3, 4, 5], number of rotations, k = 2 and indices to check, m = [1, 2]. First we perform the two rotations:
[3, 4, 5] -> [5, 3, 4] -> [4, 5, 3]

Now return the values from the zero-based indices 1 and 2 as indicated in the m array.
a[1] = 5
a[2] = 3

A jail has a number of prisoners and a number of treats to pass out to them. Their jailer decides the fairest way to divide the treats is to seat the prisoners around a circular table in sequentially numbered chairs. A chair number will be drawn from a hat. Beginning with the prisoner in that chair, one candy will be handed to each prisoner sequentially around the table until all have been distributed.

The jailer is playing a little joke, though. The last piece of candy looks like all the others, but it tastes awful. Determine the chair number occupied by the prisoner who will receive that candy.

For example, there are 4 prisoners and 6 pieces of candy. The prisoners arrange themselves in seats numbered 1 to 4. Let’s suppose two is drawn from the hat. Prisoners receive candy at positions 2, 3, 4, 1, 2, 3. The prisoner to be warned sits in chair number 3.

HackerLand Enterprise is adopting a new viral advertising strategy. When they launch a new product, they advertise it to exactly 5 people on social media.

On the first day, half of those 5 people (i.e., ) like the advertisement and each shares it with 3 of their friends. At the beginning of the second day, people receive the advertisement.

Each day, of the recipients like the advertisement and will share it with 3 friends on the following day. Assuming nobody receives the advertisement twice, determine how many people have liked the ad by the end of a given day, beginning with launch day as day 1.

For example, assume you want to know how many have liked the ad by the end of the day.

1
2
3
4
5
6

Day Shared Liked Cumulative
1      5     2       2
2      6     3       5
3      9     4       9
4     12     6      15
5     18     9      24

The cumulative number of likes is 24.

Lily likes to play games with integers. She has created a new game where she determines the difference between a number and its reverse. For instance, given the number 12, its reverse is 21. Their difference is 9. The number 120 reversed is 21, and their difference is 99.

She decides to apply her game to decision making. She will look at a numbered range of days and will only go to a movie on a beautiful day.

Given a range of numbered days, [i … j] and a number k, determine the number of days in the range that are beautiful.
Beautiful numbers are defined as numbers where |i - reverse(i)| is evenly divisible by k. If a day’s value is a beautiful number, it is a beautiful day. Print the number of beautiful days in the range.

A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, he decides to cancel class if fewer than some number of students are present when class starts. Arrival times go from on time () to arrived late ().

Given the arrival time of each student and a threshhold number of attendees, determine if the class is canceled.