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Guilford Park Knapsack Problem Mystery Cache

Hidden : 1/28/2006
Difficulty:
3 out of 5
Terrain:
4 out of 5

Size: Size:   small (small)

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Geocache Description:

Solve the puzzle for the first stage of this two-stage cache in the woods of Guilford Park. Thin trails, some off trail required, occasional thorns.

The cache is NOT at the listed coordinates, you must solve the puzzle. Here is a list of 8 projections of various lengths along with the North and West components of the total length. The units are in minutes. If you add the North component of #1 to the listed N 39 degrees 9.536 minutes you end up with N 39 9.561. (Just use simple addition here, NO spherical stuff). Your job is to select the four (different) projections that add the greatest amount in the North direction while keeping the total length less than or equal to .075.

For example, you might select #2,4,5,8 and get .020 + .015 + .010 + .005 = .050 North and a total length of .024 + .019 + .018 + .013 = .074. That is not bad, but you can do better and get farther North. Maybe you try #1,2,3,4 for .075 North but that is not allowed because the total length is .094 which is above the .075 limit. If you try #1,2,4 for .060 North and .071 total length you are wrong because I said you have to choose four projections. Don't worry about the West components yet.

#    Length  North   West
1    .028    .025    .013
2    .024    .020    .013
3    .023    .015    .017
4    .019    .015    .012
5    .018    .010    .015
6    .016    .015    .006
7    .014    .010    .010
8    .013    .005    .012

When you have found the set of 4 that get you as far North as possible without exceeding the length limit, add the 4 North values to the listed North coordinate, and now add the 4 West values to the listed West coordinate to get the location of the first stage.

The first stage is a small (1 qt) Lock-N-Lock plastic container that contains the coords of the final stage. The final stage is a smaller (1/2 qt) container. There's not much room for trade items, mainly just a log book, but it does initially contain a mini LED flashlight for FTF. Parking is in the cul-de-sac of Churchill Way. [N 39 9.325 W 76 51.843] There you will see two gray posts, one marked Howard County Park Property, which define the access to the park. An alternate parking spot is at the bridge on Murray Hill Road [N 39 9.558 W 76 51.165]. Park is open from dawn to dusk. Placed with Park permission.

Note: Not far from the final stage is Transit Satellite GC14R71.

FTF honors go to jfigel

Additional Hints (Decrypt)

[Puzzle Hint:] Qba’g hfr svefg cebwrpgvba. [Stage 1 Hint:] Ybj va n gerr ubyybj. [Stage 2 Hint:] Arfgyrq orgjrra gerr naq ebpx.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)