Counting Tiles Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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There is absolutely nothing wrong with the coordinates above. I'm sure they would take you to a very nice location where you could enjoy God's creation. However, if you want to find this cache, I don't recommend going there; I recommend solving the puzzle instead.
I have a friend who is fairly obsessive; ok, he's very obsessive. For the purpose of this puzzle, let's just call him ... ummm ... Alan.
Alan has a bunch of weird habits, not the least of which is counting tiles. If you take him into a room with square floor tiles, he will start counting them. Out loud. It's really quite annoying. As a simple example, let's assume Alan walked into a 3.x 3 closet, in which the floor tiles were each 1' x 1'. He would immediately start counting: 1-2-3-4-5-6-7-8-9. That's not so bad; but when he finished counting, he would just start counting over again: 1-2-3-... you get the idea. Very irritating.
But one day Alan had this huge epiphany: He suddenly realized that although there were nine squares, each 1' x 1', there was also one square which was 3' x 3'. So, there weren't just nine squares in the room; there were actually ten. But wait: there were also 2' x 2' squares, and after a little studying Alan determined that there were four 2' x 2' squares. So, this little room actually contained 14 squares. Alan was very proud of himself, and went back to counting. Being a mathematical guy, he noticed a pattern in the number of squares of different sizes: 9, 4, and 1. He thought it might mean something, but then realized the pattern only applied to square rooms.
Alan could count squares in fairly large rooms and never tired of counting. But then one day he saw something amazing. If there were two rooms in a house that were right next to one another, he discovered that he couldn't just add up the squares in each of the two rooms. There were actually squares that spanned the two rooms. In Alan's house, if two rooms were adjacent, there would always be an opening between the two rooms that was two feet less than the length of the shared wall. So, consider the example below: it contains two rooms: one is 6 x 8 and the other is 6 x 5. Because the shared wall is 5' long, it will have an opening between the two rooms which is 3' wide. After some study, Alan realized that in addition to the squares that were totally in one room or the other, there were also two squares which were 2' x 2' which were partially in both rooms; there were also two 3' x 3' squares spanning the two rooms. So, the total squares that Alan counted with the squares in the first room plus the squares in the second room plus the four squares that were partially in both rooms. Alan was very proud of himself ... insufferably so.
So, let's see if you are as good at counting as Alan is. He never tires of it; let's see if you do.
For this puzzle, I will give you the description of one or more rooms. You must determine the total number of squares in the rooms (including shared squares). You can assume that all rooms are rectangular, and that the length of the sides is an integer. You can also assume that all tiles in this puzzle are 1' x 1'. Use the least significant digit of the total number of squares as the digit for the coords. So, for the 3 x 3 example above which had 14 squares, you would use a '4' for the digit for the coords. But let's make it a bit easier to specify the rooms. Rather than drawing the rooms, or telling you the size, I will specify the corners of the room using (X,Y) coordinates. Since the rooms are rectangular, I just need to specify the location of upper-left and lower-right corners. So, for the 3 x 3 example above, I could specify it as (0,0), (3,3). Note I could have also specified it as (1,1), (4,4). For the example above with two rooms, I could have specified the locations as: room#1: (0,0), (6,8) and room#2: (6, 0), (12,5) .
Assume the coords are in the form: N39 AB.CDE W84 FG.HIJ. To solve for A - I, you will have to count squares for 10 different scenarios, described below. As I always say, please don't do this the hard way!
A. 1 room: (0,0), (3,3)
B. 1 room: (0,0), (6,6)
C. 2 rooms: Room#1: (0,0), (9,3) Room#2: (4,3), (10,6)
D. 3 rooms: Room#1: (0,0), (15,15) Room#2: (0,15), (19,17) Room#3: (15,0), (25,10)
E. 3 rooms: Room#1: (0,0), (1,1) Room#2: (1,1), (3,3) Room#3: (5,5), (11,363)
F. 1 room: (0,0), (12,9)
G. 2 rooms: Room#1: (10,5), (14,9) Room#2: (16,3), (19,6)
H. 3 rooms: Room#1: (2,0), (8,6) Room#2: (0,6), (6,12) Room#3: (8,2), (14,8)
I .2 rooms: Room#1: (0,0), (20,10) Room#2: (10,10), (30,20)
J. 2 rooms: Room#1: (0,0), (20,10) Room#2: (0,10), (20,20)
You can validate your puzzle solution with certitude.
Additional Hints
(Decrypt)
Unatvat va fbhgurea gerr
Treasures
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