Four-Function Loop (4Floop)

 I found out about the USPC through the Thinky Puzzles Discord and decided to try solving it this year, just to see what puzzle competitions are like. I found it to be very fun, despite having both slight nervousness and overconfidence before starting. The puzzle types introduced some new concepts to me I was surprised I hadn't seen before, especially the integration of Scrabble-like crosses in lieu of shaded squares in logic puzzles. One concept that I felt like expanding on after the competition was inspired by the choice to have a set of four puzzles each reliant individually on either the sum, difference, product, or quotient of the lengths of perpendicular runs or lines. It occurred to me that while I was familiar with mystery operation puzzles through KenKen and Math Path, I had not seen a mystery operation that related to perpendicular lines.

I started making this ruleset using only the four basic operations in a sort of variant Balance Loop, before realizing that the Balance Loop rules were hindering the logic and making it just about the numbers. Eventually I pondered what it would mean for the line to travel straight through a number, and decided to incorporate square roots. This felt reasonable enough and allowed the path to travel straight through unknown numbers, which I liked. At some point, I was reminded of the dubiously-named "four-function calculator". I consider it dubious because the formal College Board definition suggests that they should also be able to do square roots and percents, for a total of six operations. This was when I decided square roots were not cursed enough and incorporated percents. They were restricted enough that their inclusion didn't break any of my earlier puzzles and allowed me to focus on a much larger puzzle dedicated to them.

Link

Rules:  Draw a loop that passes through every number and question mark. If the loop turns at a number, that number is either the sum, difference, product, or quotient of the two lengths of segments that protrude from it. If the loop passes straight through a number, that number is either the square root or percent amount (x100) of that segment's length.