## Drawing Book

A teacher asks the class to open their books to a page number. A student can either start turning pages from the front of the book or from the back of the book. They always turn pages one at a time. When they open the book, page 1 is always on the right side: When they flip page 1, they see 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 a student

## Counting Valleys

An avid hiker keeps meticulous records of their hikes. During the last hike that took exactly steps steps, for every step it was noted if it was an uphill, U, or a downhill, D step. Hikes always start and end at sea level, and each step up or down represents a 1 unit change in altitude. We define the following terms: A mountain is a sequence of consecutive steps above sea level, starting with a step up from sea level and ending with a step down to sea level. A valley is a sequence of consecu

## Electronics Shop

A person wants to determine the most expensive computer keyboard and USB drive that can be purchased with a give budget. Given price lists for keyboards and USB drives and a budget, find the cost to buy them. If it is not possible to buy both items, return -1. Example b = 60 keyboards = [40, 50, 60] drives = [5, 8,12] The person can buy a 40 keyboards + 12 USB drives = 52, or a 50 keyboards + 8 USB drives = 58. Choose the latter as the more expensive option and return 58. Function

## Cats and a Mouse

Two cats and a mouse are at various positions on a line. You will be given their starting positions. Your task is to determine which cat will reach the mouse first, assuming the mouse does not move and the cats travel at equal speed. If the cats arrive at the same time, the mouse will be allowed to move and it will escape while they fight. You are given q queries in the form of x, y, and z representing the respective positions for cats A and B, and for mouse C. Complete the function catAndMou

## Forming a Magic Square

We define a magic square to be an n * n matrix of distinct positive integers from 1 to n^2 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 * 3 matrix s 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