All of Licht's Comments + Replies

Puzzle: 1

(It was my first time trying tags, I had the problem set tag in mind. I also intended for it to be a timed test, but realized that it might be to on the nose. )

It is a formatting error though and I've had to go back and edit a couple times to understand where I should make discrepancies in the text so that things aren't left open ended. In certain cases defining certain aspects has changed the answer, but now I know the specificity needed for these types of exercises.

Puzzle: 1

(I corrected the answer I gave for the first part, thank you) The answer needs a slight specification in that the r is not that of the night-watches observable field, but r+epsilon, indicating that the spy remains one point beyond the FOV of the night-watch.

2Dagon12dYou specify that the vision is a sharp cutoff, so it's an infinitessimally small difference (will be referred to as "epsilon" when you get to calculus), which rounds to 0 in this problem, for any precision of r.
Puzzle: 1

Thank you for the comment, I will try to incorporate some of the suggestions into the puzzle to help with clarity. 

1) a. The night-watch is stationary, there are only two paths which you can take that will get you to the wall in the quickest possible way. b. Once in the field of view of the night-watch the alarm will raise and your cover blown. 

2) You understand correctly. 

3) They are situated on the wall.

2Measure12dIn that case, I get a different answer: The shortest path to the wall avoiding the semicircular FOV is a quarter-circle with length pi/2 times r (arriving at a distance r from the night watch).
[Prediction] What war between the USA and China would look like in 2050

I think one factor that was overlooked as a potential for conflict is the developments by Russia and the ongoing push by China to be involved in the Arctic. As you mentioned they are interested in material collection and with the melting ice caps this unleashes a plentiful lot, along with new shipping routes. They have been granted an observer seat on the arctic council and with more military activity in the north with Russia and the rest of the arctic powers, it is not far off that this area will become more engaged here.