Lilah has a string, s, of lowercase English letters that she repeated infinitely many times.

Given an integer, n, find and print the number of letter a’s in the first n letters of Lilah’s infinite string.

For example, if the string s = ‘abcac’ and n = 10, the substring we consider is abcacabcac, the first 10 characters of her infinite string. There are 4 occurrences of a in the substring.

Your local library needs your help! Given the expected and actual return dates for a library book, create a program that calculates the fine (if any). The fee structure is as follows:

1. If the book is returned on or before the expected return date, no fine will be charged (i.e.: fine = 0.
2. If the book is returned after the expected return day but still within the same calendar month and year as the expected return date, fine = 15 Hackos x (the number of days late).
3. If the book is returned after the expected return month but still within the same calendar year as the expected return date, the fine = 500 Hackos x (the number months late).
4. If the book is returned after the calendar year in which it was expected, there is a fixed fine of 10000 Hackos.

Charges are based only on the least precise measure of lateness. For example, whether a book is due January 1, 2017 or December 31, 2017, if it is returned January 1, 2018, that is a year late and the fine would be 10000 Hackos.

Watson likes to challenge Sherlock’s math ability. He will provide a starting and ending value describing a range of integers. Sherlock must determine the number of square integers within that range, inclusive of the endpoints.

Note: A square integer is an integer which is the square of an integer, e.g. 1, 4, 9, 16, 25.

For example, the range is a = 24 and b = 49, inclusive. There are three square integers in the range: 25, 36 and 49.

You have a string of lowercase English alphabetic letters. You can perform two types of operations on the string:

1. Append a lowercase English alphabetic letter to the end of the string.
2. Delete the last character in the string. Performing this operation on an empty string results in an empty string.

Given an integer, k, and two strings, s and t, determine whether or not you can convert s to t by performing exactly k of the above operations on s. If it’s possible, print Yes. Otherwise, print No.

For example, strings s = [a, b, c] and t = [d, e, f]. Our number of moves, k = 6. To convert s to t, we first delete all of the characters in 3 moves. Next we add each of the characters of t in order. On the move, you will have the matching string. If there had been more moves available, they could have been eliminated by performing multiple deletions on an empty string. If there were fewer than 6 moves, we would not have succeeded in creating the new string.

An integer d is a divisor of an integer n if the remainder of n / d = 0.

Given an integer, for each digit that makes up the integer determine whether it is a divisor. Count the number of divisors occurring within the integer.

Note: Each digit is considered to be unique, so each occurrence of the same digit should be counted (e.g. for n = 111, 1 is a divisor of 111 each time it occurs so the answer is 3).

The factorial of the integer n, written n!, is defined as:

n! = n x (n - 1) x (n - 2) x ... x 3 x 2 x 1

Calculate and print the factorial of a given integer.

For example, if n = 3, we calculate 30 x 29 x 28 x ... x 3 x 2 x 1 and get 265252859812191058636308480000000.

Aerith is playing a cloud hopping game. In this game, there are sequentially numbered clouds that can be thunderheads or cumulus clouds. Her character must jump from cloud to cloud until it reaches the start again.

To play, Aerith is given an array of clouds, c and an energy level e = 100. She starts from c[0] and uses 1 unit of energy to make a jump of size k to cloud c[(i + k) % n]. If Aerith lands on a thundercloud, c[i] = 1, her energy (e) decreases by 2 additional units. The game ends when Aerith lands back on cloud 0.

Given the values of n, k, and the configuration of the clouds as an array c, can you determine the final value of e after the game ends?

For example, give c = [0, 0, 1, 0] and k = 2, the indices of her path are 0 -> 2 -> 0. Her energy level reduces by 1 for each jump to 98. She landed on one thunderhead at an additional cost of 2 energy units. Her final energy level is 96.

Note: Recall that % refers to the modulo operation. In this case, it serves to make the route circular. If Aerith is at c[n -1] and jumps 1, she will arrive at c[0].

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