This is my first puzzle cache, hidden by myself and MizPiggy, using mathematics puzzles. The cache IS NOT at the posted coordinates, but the coordinates ARE for a good place to park for this cache. Lots of stealth will be required, as muggles constantly pass this area. The puzzles are written after this short background for The Dilly Line.
Ouston-Pelaw Dilly Line (Wagonway) Background
The Ouston-Pelaw Wagonway (Dilly Line) was in what is now Gateshead's patch from Birtley to Pelaw passing through High Heworth to take Heworth Colliery coal to the staithes at Pelaw. The name Dilly (sometimes spelt as Dilley) Line is not exclusive to this line and indeed there was one from Throckley to Lemington. If you follow that link you'll see that the author says the name derives from the steam engine that pulled the trucks but that's not universally true..indeed the Ouston Pelaw line had no truck- pulling steam engine . Is it the truck, the engine or the line that is the dilly. All three, it would appear. From Madagascar we have "In bituminous coal mining....a dilly (light wagon, truck, or water cart) used to haul coal or water underground or at the surface of a mine....". In Wylam we have all the locomotives being called dillies. Joseph Wright's English dialect dictionary allows these and the counter balancing system where no locomotive is involved.
DILLY (N.). A counter-balance mounted upon two pairs of tram wheels by means of which the empty tubs are carried up an underground incline of a greater inclination than 1 in 3.
Source: http://www.gateshead-history.com/ouston-pelaw-dilly-line.html
The cache is at the following coordinates:
N54 AB.CDE
W001 FG.CEF
The Puzzles:
1) A3 = 125 Solve for A
2) 36 = B2 Solve for B
3) 23 = C Solve for C
4) 32 - 2 = D Solve for D
5) 16 x E = 64 Solve for E
6) (4+(3x3))-10 = F Solve for F
7) (7+(GxG))-4 = 7 Solve for G
You can validate your puzzle solution with certitude.
Congratulations to "C's" for the FTF!