Alice is playing an arcade game and wants to climb to the top of the leaderboard and wants to track her ranking. The game uses Dense Ranking, so its leaderboard works like this:

• The player with the highest score is ranked number on the leaderboard.

• Players who have equal scores receive the same ranking number, and the next player(s) receive the immediately following ranking number.

For example, the four players on the leaderboard have high scores of 100, 90, 90, and 80. Those players will have ranks 1, 2, 2, and 3, respectively. If Alice’s scores are 70, 80 and 105, her rankings after each game are and .

Given a sequence of n integers, p(1), p(2), ..., p(n) where each element is distinct and satisfies . For each x where , find any integer y such that p(p(y)) and print the value of y on a new line.

For example, assume the sequence p = [5, 2, 1, 3, 4]. Each value of x between 1 and 5, the length of the sequence, is analyzed as follows:

1. x = 1 p[3], p[4] = 3, so p[p[4]] = 1
2. x = 2 p[2], p[2] = 2, so p[p[2]] = 2
3. x = 3 p[3], p[5] = 4, so p[p[5]] = 3
4. x = 4 p[5], p[1] = 5, so p[p[1]] = 4
5. x = 5 p[1], p[3] = 1, so p[p[3]] = 5

The values for yare [4, 2, 5, 1, 3].

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.

The Utopian Tree goes through 2 cycles of growth every year. Each spring, it doubles in height. Each summer, its height increases by 1 meter.

Laura plants a Utopian Tree sapling with a height of 1 meter at the onset of spring. How tall will her tree be after n growth cycles?

For example, if the number of growth cycles is n = 5, the calculations are as follows:

1
2
3
4
5
6
7

Period  Height
0          1
1          2
2          3
3          6
4          7
5          14

When you select a contiguous block of text in a PDF viewer, the selection is highlighted with a blue rectangle. In this PDF viewer, each word is highlighted independently. For example:

In this challenge, you will be given a list of letter heights in the alphabet and a string. Using the letter heights given, determine the area of the rectangle highlight in assuming all letters are 1mm wide.

For example, the highlighted word = torn. Assume the heights of the letters are t = 2, o = 1, r = 1 and n = 1. The tallest letter is 2 high and there are 4 letters. The hightlighted area will be 2 * 4 = 8 so the answer is 8.

Dan is playing a video game in which his character competes in a hurdle race. Hurdles are of varying heights, and Dan has a maximum height he can jump. There is a magic potion he can take that will increase his maximum height by 1 unit for each dose. How many doses of the potion must he take to be able to jump all of the hurdles.

Given an array of hurdle heights height, and an initial maximum height Dan can jump, k, determine the minimum number of doses Dan must take to be able to clear all the hurdles in the race.

For example, if height = [1, 2, 3, 3, 2] and Dan can jump 1 unit high naturally, he must take 3 - 1 = 2 doses of potion to be able to jump all of the hurdles.