Rules #3 and #4 give us the following setup: __ __ __ __ __ G __ K __ M A M J J A S O N
Rule #1 tells us that we must go through headquarters before switching mines, so we can conclude that September has to be spent at headquarters, giving us: __ __ __ __ __ G H K __ M A M J J A S O N
Following this same rule, we know that November cannot be G (as October is K and we can't have KG placed consecutively since we need to go through headquarters before switching mines). This means that November must be either K or H.
Now, remember the original setup explicitly tells us that the team will work at G for 3 months and at K for 3 months. It then gives us options of 9 months, saying that the months not spent at a mine will be spent at headquarters. Therefore, we will have a total of 3 months spent at headquarters.
If we assign H to November, we will have used 2 of our 3 total months at headquarters within only the last 3 of our 9 months. It would then be impossible to fill months March-July with only 1 available H. This is because we have to utilize H when we switch between different mines and when we need to break up more than two consecutive months spent at the same mine. Therefore, we can deduce that November cannot be spent at headquarters. This leaves K as the only remaining option for November.
Does that make sense? Hope it helps! Please let us know if you have any other questions!
