DANGEROUS MANEUVERS Somewhere in the Mojave Desert, the army set up training cam
ID: 3141830 • Letter: D
Question
DANGEROUS MANEUVERS
Somewhere in the Mojave Desert, the army set up training camps named Arachnid, Feline, Canine, Lupine, Bovine, and Thirty-Nine. Several camps are connected by roads:
Arachnid is 15 miles from Canine, Bovine is 12 miles from Lupine,
Feline is 6 miles from Thirty-Nine, Lupine is 3 miles from Canine,
Bovine is 9 miles from Thirty-Nine, Bovine is 7 miles from Canine, Thirty-Nine is 1 mile from Arachnid, and Feline is 11 miles from Lupine.
No other pairs of training camps are connected by roads.
Answer each of the following questions (in each answer, indicate both the mileage and the route): What is the shortest route from
Feline to Bovine?
Canine to Thirty-Nine?
Lupine to Thirty-Nine?
Lupine to Bovine?
Canine to Feline?
Arachnid to Feline?
Arachnid to Lupine?
Feline to Bovine?
Canine to Thirty-Nine?
Lupine to Thirty-Nine?
Lupine to Bovine?
Canine to Feline?
Arachnid to Feline?
Explanation / Answer
The following is the sorted list of roads where the camps are denoted by their first letter:
(i) Feline to Bovine: Feline is connected to Thirty-nine and Lupine of which the road to Thity-nine is shorter. Further Thirty-nine is connected to Bovine.
So the shortest route = Feline -> Lupine -> Bovine with a distance of 6 + 9 = 15 miles.
(ii) Canine to Thirty-nine: Both routes via Bovine and Arachnid are of 16 miles each. They are both the shortest routes. (If Lupine is chosen, the routes from Lupine are all greater than 16)
(iii) Lupine to Thirty-nine: By previous result, if we travel via Canine, it takes 3 + 16 = 19 and via Feline 11 + 6 = 17.
The shortest route is Lupine -> Feline -> Thirty-nine which is of 17 miles.
(iv) Lupine to Bovine: Since the shortest roads from Lupine and to Bovine are both via Canine, the shortest route is Lupine -> Canine -> Bovine which is 3 + 7 = 10 miles.
(v) Canine to Feline: The route via Lupine takes 3 + 11 = 14 miles. The route via Bovine takes 7 + 9 = 16 miles as per the result of 1.
So the shortest route is Canine -> Lupine -> Feline which is of 14 miles.
(vi) Arachnid to Feline: Since the shortest roads from Arachnid and to Feline are both via Thirty-nine, the shortest route is Arachnid -> Thirty-nine -> Feline which is 1 + 6 = 7 miles.
(vii) Arachnid to Lupine: The route via Canine takes 15 + 3 = 18 miles. We saw that the shortest distance from Arachnid to Feline is 7 miles. The distance from Feline to Lupine is 11 miles which also adds up to 18 miles.
Thus both routes are shortest and take 18 miles.
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