The Winchester Transit Authority operates a bus line with seven stops -- A,
B, C, D, E, F, and G.
Here are some clues about the seven bus stops:
From A to B is 2 miles.
From A to D is 7 miles.
From C to E is 3 miles.
From C to G is 7 miles.
From E to F is 2 miles.
From E to G is 4 miles.
B is 4 miles due southwest of C.
D is 5 miles due southeast of B.
F is 4 miles due northeast of D.
The bus begins its route at A and passes every stop once before returning to A,
following the shortest path possible.
Unlike most buses, this one always travels in a straight line between stops, and
straight roads exist between every possible pair of bus stops.
If the bus stops at B sometime before it stops at C, in what sequence does the bus
pass the stops?
Solution to the Problem:
The bus route is A-B-D-G-F-E-C and then back to A.Use a piece of graph paper to help solve this problem. Use the last three clues to begin plotting the points C, F, D, and B. From these last three clues, CFDB must be a rectangle. Hence, CF is 5 miles long and parallel to BD. Since CE is 3 miles and EF is 2 miles, E must be a point on line CF. CG is 7 miles, CE is 3 miles, and EG is 4 miles, so CEFG is a straight line. G must be 2 miles southeast of corner F of the rectangle.
AD is 7 miles, AB is 2 miles, and BD is 5 miles, so ABD is a straight line, and A is 2 miles northwest of corner B of the rectangle.
It's now easy to see that the shortest route that passes every bus stop travels from A through B, D, G, F, E, and C, or the reverse. Since the bus stops at B before C, this is in fact the route.
Correctly solved by:
| 1. Akash Patel | Columbus, Georgia |
| 2. Jeffrey Gaither *** | Winchester, Virginia |
| 3. Walt Arrison *** | Philadelphia, Pennsylvania |
| 4. Richard Johnson | LaJolla, California |
| 5. Keith Mealy | Cincinnati, Ohio |
| 6. John Funk | Ventura, California |
| 7. James Alarie *** | University of Michigan -- Flint, Flint, Michigan |
| 8. Jim Kennedy | Limerick, Ireland |
| 9. G. Beavers | ---------- |
| 10. Chris McCormick | Winchester, Virginia |
| 11. Andrew Oliver | Winchester, Virginia |
| 12. Viktor Bergqvist | Tullängen, Sweden |