Answer to November 2, 1998 Problem |
---|
A Walk in Winchester A map of downtown Winchester is shown below. Billy lives at the corner of Monmouth and Stewart. Betty lives at the corner of Cameron and Boscawen. Billy decides that he will visit Betty every day after school until he has tried every different route from his house to her house. Billy travels only east and north. How many different routes can Billy take to Betty's house? Boscawen +---+---+---+---O---+ | | | | | | Cork +---+---+---+---+---+ N | | | | | | ^ Clifford +---+---+---+---+---+ | | | | | | | W <--+--> E Cecil +---+---+---+---+---+ | | | | | | | ! Leicester +---+---+---+---+---+ S | | | | | | Monmouth O---+---+---+---+---+ | | | | | | S W B L C K t a r o a e e s a u m n w h d d e t a i d o r r n o u o t g c n n t k o n |
---|
Boscawen 1---6--21--56--126--+ | | | | | | Cork 1---5--15--35--70---+ N | | | | | | ^ Clifford 1---4--10--20--35---+ | | | | | | | W <--+--> E Cecil 1---3---6--10--15---+ | | | | | | | ! Leicester 1---2---3---4---5---+ S | | | | | | Monmouth 1---1---1---1---1---+ | | | | | | S W B L C K t a r o a e e s a u m n w h d d e t a i d o r r n o u o t g c n n t k o nAlternate solution C. W. Larson from Northern Arizona University wrote that Billy can only take one route to Betty's house since by travelling only north and east, once he gets to Betty's house, he can never return to his own! |
---|
1. Christophe W. Larson | Flagstaff, AZ (Northern Arizona University) |
2. Trey Genda | Winchester, VA |