Congrats to HoLLeTT> on FTF!
If you aren't familiar with this kind of puzzle, you may want to try solving GC61BVX: (NSML02: a Micro Logic Tutorial) first.
This puzzle involves modular arithmetic, which is the same sort of math you do when you read a clock. Clocks are "mod 12", meaning that 2 hours after 11, it is 1. That is 11+2 ≡ 1. Similarly, 5 hours before 2 is 9, or 2-5 ≡ 9.
This puzzle is like using a clock with the hours marked 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Instead of writing 10, you would write 0. I am using the "≡" to indicate that the answer on the right side must be one of the digits 0-9, obtained using modular arithmetic like in the examples. So here are more examples with "mod 10" math, which is used for this problem:
5+2 ≡ 7 and 5+5 ≡ 0 and 5-7 ≡ 8. To see the last one, note that 5-7 = -2 and when you go below "0" you start again at "9".
When you calculate something on the left side, and it is bigger than 9, you get the equivalent number by subtracting away 10 repeatedly until you get a number between 0 and 9. If your left side answer is less than 0, add 10 until you get a number between 0 and 9. So 7*8 ≡ 6 since we know that 7*8 =56, and 4*(3-6) ≡ 8 because 4*(3-6) = 4*(-3) = -12.
You can get the coordinates by solving the following: The ten letters (A, B, C, D, E, F, G, H, J, K) represent the digits from 0 to 9. No two letters are equal. "G*A" represents multiplication and "GA" represents a two-digit number. So if G=7 and A=3, then GA=73 and G*A=21. Remember that the answer on the right represents a "mod 10" answer.
G + G ≡ B
G – G ≡ B
F * K ≡ H
H * K ≡ F
D / C ≡ A
H + J ≡ C
E = ???
The geocache is hidden at N 45 05.X, W 064 23.Y, where ....
X = JHG + DK and Y = FCB + EA
You can check your answer below.
