Longtown Castle is on the border with Herefordshire and Wales and sits below the Hatterall Ridge and the Offa's Dyke path. It is a classic Motte and Bailey castle. More information can be found on the CastleWales site To find the final cache location, you need to find two intermediate clues.
First Clue
At the initial location, look for the Old School House and the display of the original benefactors. How much did Mr Henry Harris donate (in L S D), in the format X Y Z. The second site is at N 51 57.38(X+Y) W 002 59.(X+Y)Y6
Second Clue
At the information board find the dates when the keep was build, from 1216 until ABCD. The next site is at N 51 57.(A-D)7(B*C) W 002 59.C(B*2)6
Third (and last) Clue
From this info board, what figure was the population greater than in 1310 ? Using these numbers in the format EFG, stand behind the board and face the keep. Take (E*4) steps at 135% to the right (back over your right shoulder and you will find the cache.
The cache is a small plastic box with a log book (but no pen) and some items for exchange.