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 Going Downtown (Posted on 2006-11-08)
The Downtown area of Grid City consists of 10 intersecting streets in a 5x5 grid. Most of the intersections are 4-way, but exactly one intersection on each street is actually an overpass, one street going over the other, forcing drivers to keep straight.

Four different men (with license plates 5, 7, 8, and 9) enter and exit downtown in different spots. Some facts about their routes are as follows:

• No driver enters the same intersection more than once.
• At each non-overpass intersection, all drivers that entered it from north/south turned a certain way (right or left) at that particular intersection, and all drivers that entered it from east/west turned the opposite way.
• The number of turns each driver made downtown equals the number on his license plate.
Given this map of the region, where does 5 exit downtown, and what paths do each of them take?
```          7       9
|   |   |   |   |
9-+---+---+---+---+-
|   |   |   |   |
-+---+---+---+---+-7
|   |   |   |   |
-+---+---+---+---+-8
|   |   |   |   |
-+---+---+---+---+-
|   |   |   |   |
8-+---+---+---+---+-
|   |   |   |   |
5      ```

 See The Solution Submitted by Gamer Rating: 4.2500 (4 votes)

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 Solution | Comment 4 of 7 |
I think I've got a setup that works.  However, there are two different possible exit points for the #5 car...

I'll use + to indicate an intersection with an overpass, / to indicate an intersection where the north-south cars turn right, and \ to represent an intersection where the north-south cars turn left.  If it helps, picture the cars as lasers being reflected off of mirrors or something...

`      7   99 \ / / \ +  \ \ + \ / 7  + \ / \ / 8  / + / \ / 8 /     +           5`

I've intentionally left some of the intesections blank because they are not in the path of the 7, 8, and 9 cars.  Depending on how you set up these missing intersections, the 5 car could follow two separate paths:

`      7   99 \ / / \ +  \ \ + \ / 75 + \ / \ / 8  / + / \ / 8 / \ / +           5Or:      7   99 \ / / \ +  \ \ + \ / 7    \ / \ / 8  / + / \ / 58 /   \ + /          5 `

 Posted by tomarken on 2006-11-08 21:13:23

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