Several gnomes that live in the National Capital Region have found
a crystal ball in an abandoned mine shaft in Gatineau Park. It
allows them see into the future! On your way to GAG11
- Mine you spot the 6 gnomes: Nobwick, Loopwinkle, Bunknor,
Murpen, Pilbert, and Ruggles. They are huddled around the crystal
ball. You ask them "what are you crazy gnomes doing?" Ruggles
replies, "we're using the crystal ball to get the winning lottery
numbers for the next Lotto Max drawing." You reply "Silly gnomes,
you can't buy lottery tickets; you don't have the proper
identification. I'll tell you what I'll do. I'll buy the ticket for
you on the condition that you let me keep 50% of the winnings."
The gnomes all looked at each other and begin conversing in an
unknown language. When they finally finish, Ruggles turns to you
and says "we have talked it over and we want you to be our partner
in this endeavor. However you will have to prove that you are smart
enough so that we know you will be smart with the winnings. We
won't give you the winning numbers, but we each have a clue for
you. If you are smart, you will be able to use those clues to
determine the winning numbers."
Nobwick's Clue: Let the winning
numbers be A, B, C, D, E, F, G such that 1 <= A < B < C
< D < E < F < G <= 49
Loopwinkle's Clue: Let P = A * B
* C * D * E * F * G
Bunknor's Clue: Let S = A + B +
C + D + E + F + G
Ruggles' Clue: Let X be the
number of combinations that yield S. In other words, of all
possible A, B, C, D, E, F, G, let X be the number of combinations
where A + B + C + D + E + F + G equals the sum of the winning
numbers.
Murpen's Clue: This condition is
satisfied by the winning numbers: P = S * X
Pilbert's Clue: P of the winning
numbers satisfies this condition: 125,000,000 < P <
175,000,000
Ruggles goes on to say "we have hidden a geocache (a small
"Lock-and-Lock" container) in Gatineau park for you to put the
winnings in. It can be found at the following location (A through G
are the winning numbers from above in ascending order): "
T = (E * C) + D - (B -
A)
R = ((A) * ((F * G) - (E * G))) -
(3 * G) + (2 * A) + B
N 45 29.T W 075 48.R
Warning in the distant past there was
a barbed wire fence close to where the cache is hidden. One or more
trees in the area grew around the fence. The fence has been taken
down, but fragments of wire remain embedded in some trees.