PROBLEM's
1: Santa is trying to deliver presents in a large apartment building, but he can't find the right floor - the directions he got are a little confusing. He starts on the ground floor (floor 0) and then follows the instructions one character at a time.
An opening parenthesis, (, means he should go up one floor, and a closing parenthesis, ), means he should go down one floor.
The apartment building is very tall, and the basement is very deep; he will never find the top or bottom floors.
For example:
(()) and ()() both result in floor 0.
((( and (()(()( both result in floor 3.
))((((( also results in floor 3.
()) and ))( both result in floor -1 (the first basement level).
))) and )())()) both result in floor -3.
To what floor do the instructions take Santa?
2: Now, given the same instructions, find the position of the first character that causes him to enter the basement (floor -1). The first character in the instructions has position 1, the second character has position 2, and so on.
For example:
) causes him to enter the basement at character position 1.
()()) causes him to enter the basement at character position 5.
What is the position of the character that causes Santa to first enter the basement?
3: I Was Told There Would Be No Math The elves are running low on wrapping paper, and so they need to submit an order for more. They have a list of the dimensions (length l, width w, and height h) of each present, and only want to order exactly as much as they need.
Fortunately, every present is a box (a perfect right rectangular prism), which makes calculating the required wrapping paper for each gift a little easier: find the surface area of the box, which is 2*l*w + 2*w*h + 2*h*l. The elves also need a little extra paper for each present: the area of the smallest side.
For example:
A present with dimensions 2x3x4 requires 2*6 + 2*12 + 2*8 = 52 square feet of wrapping paper plus 6 square feet of slack, for a total of 58 square feet.
A present with dimensions 1x1x10 requires 2*1 + 2*10 + 2*10 = 42 square feet of wrapping paper plus 1 square foot of slack, for a total of 43 square feet.
All numbers in the elves' list are in feet. How many total square feet of wrapping paper should they order?