Puzzle: 1

(I have been wanting to try my hand at creating puzzles to be done quick for some time now and here is my first attempt. I don’t know yet how to rank its difficulty, so I will let you try and let me know what you think. I would also appreciate any feedback or suggestions on how I can improve, i.e. how to make it more challenging, where things were to obvious, how I might better word the puzzle to hide the logic, that sort of thing. Thank you, and have fun!)

The puzzle should be done as quickly as possible (and try your hand at doing it without pen and paper), so set a timer once you have red and understood the question to see how long it takes you, and have fun!

You are a spy that is standing in front of a wall of infinite length. Your mission is to infiltrate the enemy, by getting past the wall, and put a stop to a life threatening event. Directly in front of you stands the night-watch, who although stationary, is able to see everything in all directions in front of the wall on which they stand, and right up to a point behind which you stand.

You have to infiltrate the enemy as fast as possible, for if you don’t, the population on earth will be dramatically altered. Once at the wall you have the espionage acumen to get past flawlessly and carry out the mission, but if caught by the night-watch at any point before reaching the wall, the alarm is raised immediately and you will fail the mission.

The question is: What is the distance you move to infiltrate the wall in the quickest time possible, without being detected by the night-watch?

Bonus: How far away from the night-watch are you when you have infiltrated the enemy?

(The answers are below)

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Main question: The distance that the spy will travel from their starting point, to arrive the quickest to the wall, and at which point they wont get the night-watches attention, is

Bonus question: They will arrive at the wall at a distance equal to the sight of the night watch plus their position point just beyond that. .