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.

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 mm² 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 = 8mm² so the answer is 8.

Given an array of integers, find and print the maximum number of integers you can select from the array such that the absolute difference between any two of the chosen integers is less than or equal to 1. For example, if your array is a = [1,1,2,2,4,4,5,5,5], you can create two subarrays meeting the criterion: [1,1,2,2] and [4,4,5,5,5]. The maximum length subarray has 5 elements.

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

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).

Brie’s Drawing teacher asks her class to open their books to a page number. Brie can either start turning pages from the front of the book or from the back of the book. She always turns pages one at a time. When she opens the book, page 1 is always on the right side:

When she flips page 1, she sees pages 2 and 3. Each page except the last page will always be printed on both sides. The last page may only be printed on the front, given the length of the book. If the book is n pages long, and she wants to turn to page p, what is the minimum number of pages she will turn? She can start at the beginning or the end of the book.

Given n and p, find and print the minimum number of pages Brie must turn in order to arrive at page p.

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 5^th day.

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 (arrivalTime <= 0) to arrived late (arrivalTime > 0).

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