Finding Your Routes. By: "Carl G." News: rec.puzzles Gridtown consists of 20 square blocks, formed by six north-south streets (called "A Street" through "F Street")and five east-west streets (call "1st Avenue" through "5th Avenue"). Seven postmen walk seven different routes that are each exactly seven blocks long. When they walk down a street they deliver mail to both sides of the street. The postmen each start and end their routes at an intersection (e.g., the corner of A St. and 2nd Ave. = A2). Can you find a set of seven routes that will allow the postmen to deliver mail to all of Gridtown? Each route must consist of a contiguous path that is exactly seven blocks long. Every side of every block must be visited at least once. Map of Gridtown (best viewed with a fixed-width font). A B C D E F 1 *---*---*---*---*---* . | | | | | | 2 *---*---*---*---*---* . | | | | | | 3 *---*---*---*---*---* . | | | | | | 4 *---*---*---*---*---* . | | | | | | 5 *---*---*---*---*---* Carl G. SPOILER SPOILER - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Here is a solution - the paths are labelled with the digits 1 through 7. +1111+1111+1111+1111+1111+ 1 2 3 4 5 1 1 2 3 4 5 1 1 2 3 4 5 1 +2222+3333+4444+5555+6666+ 2 3 4 5 6 6 2 3 4 5 6 6 2 3 4 5 6 6 +2222+3333+4444+5555+6666+ 2 2 3 4 5 6 2 2 3 4 5 6 2 2 3 4 5 6 +2222+3333+4444+5555+6666+ 7 3 4 5 6 7 7 3 4 5 6 7 7 3 4 5 6 7 +7777+7777+7777+7777+7777+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Special Configuration: By: "Justin Leck" Date: Tue, 26 Sep 2000 17:55:30 +0100 Forbidden path pattern: 1 1 2 2 or 1 1 1 1 which produced only two possible solutions. Hint: Each solution is rotationally symmetrical but not vertically or horizontally symmetrical. SPOILER 1 1 2 3 3 1 4 1 2 5 3 4 1 2 5 6 4 1 2 5 6 3 1 2 5 6 7 4 2 5 6 7 3 2 5 6 7 3 4 5 6 7 3 7 4 4 6 7 7 1 1 1 1 2 1 3 4 2 1 2 5 3 4 2 1 5 5 3 4 2 2 6 5 3 4 2 6 6 5 3 4 4 7 6 5 3 4 6 7 6 5 3 7 6 7 7 7 7