1st of April Mystery Cache

Aprils Fools' Day is celebrated throughout the world on the 1st of April by playing practical jokes or hoaxes on each other. It's a day when you can expect that most things you hear from friends aren't really true. Some would avoid usual activities like Geocaching on a day like this. Some are braver than others.

I have placed a small box to honor this day but of course it's not at the given coordinates (where would be the fun in that?). You will find the box at N 44 25.ABC E 026 05.DEF and also you have below everything you need to find A, B, C, D, E and F a bit extra. The problem is that only 1/3 of the following 18 statements are true, the rest are hoaxes.

01) C is F-B
02) D is E-C
03) B is C-D
04) E is 6
05) F is A-B-D
06) B is E/4
07) A is F-D
08) B is 7
09) C is E-D
10) F is 5
11) C is A/2
12) D is E-8
13) D is B/4
14) A is B+1
15) F is E*3/2
16) E is F+3
17) E is A-3
18) A is C*C

Given the circumstances, I think a bit of trial and error is to be expected so I strongly recommend using this Geochecker for this one.

From the final location you will have a perfect view to one famous building where every day of the year is the 1st of April.