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Gammon Gambit Mystery Cache

Difficulty:
2 out of 5
Terrain:
1 out of 5

Size: Size:   micro (micro)

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Geocache Description:

The cache is not located at the coordinates above (kids, don't play on the freeway).

Another cache in my board game series, which consists of:
Boggle Academy
Battle Stations [archived 12/2009]
Word Freak
Chance Encounter [archived 8/2011]
Gammon Gambit
Domino Delight

To get the correct coordinates, you'll need to answer a few simple questions about the backgammon game in progress below. The game follows the standard rules of backgammon (see user's web page).

It looks like white is in a bit of trouble. Tough prime there, red. How many covered points are in red's prime? Let that number = a

White is on the bar. White is moving clockwise. How many rolls are there that will put white in play from the bar, given the board's current configuration? Let that number = b

Ignoring any moves that white might be able to make to slow red down, what is the minimum number of rolls red could make to win the game? Let that number = c

Earlier in the game, white doubled the stakes of the game (note the cube in picture). Therefore, red now has control of the cube. If red uses the cube (and white accepts), how many points would the game now be worth? Let that number = d

Finally, b + 1 = e

The cache container, a key box, is located at N 47 42.b(c+d)(a+d-e) and W 122 19.ac(d-e). Congratulations to Old Bald Eagle for another FTF!

You can check your answers for this puzzle on Geochecker.com.

Additional Hints (Decrypt)

yhk

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)