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.

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.

We define a magic square to be an n x m matrix of distinct positive integers from 1 to where the sum of any row, column, or diagonal of length n is always equal to the same number: the magic constant.

You will be given a 3 x 3 matrix of integers in the inclusive range [1, 9]. We can convert any digit a to any other digit b in the range [1, 9] at cost of |a - b|. Given s, convert it into a magic square at minimal cost. Print this cost on a new line.

Note: The resulting magic square must contain distinct integers in the inclusive range [1, 9].

For example, we start with the following matrix s:

1
2
3

5 3 4
1 5 8
6 4 2

We can convert it to the following magic square:

1
2
3

8 3 4
1 5 9
6 7 2

This took three replacements at a cost of |5 - 8| + |8 - 9| + |4 - 7| = 7.