The downtown area of Truth Town is represented by a 6x6 grid of streets, as shown in the map below, where each cell represents an intersection of north/south and east/west streets.



One tourist decided to enter downtown at the lower left, drive around before stopping for lunch at the intersection marked in orange, and then drive around some more before exiting in the upper right.

The tourist managed to drive through every intersection once, except for the intersections marked in yellow where he drove straight through both cross streets (north/south and east/west). What route did he end up choosing?

(Hint: He travelled the same distance before eating lunch as after eating lunch.)

my reasoning used was to draw out the grid, then draw lines going through all yellow squares as we know the path had to move these squares in exactly this way.  Then, since all remaining squares are visited only once, I was able to construct the rest of the path.  Starting at the lower left square, the following gives the path where
U - move up
D - move down
L - move left
R - move right
[m] move m is into a yellow square
(m) move m is into the lunch square

UR[R]R[R]DRUUUL[L]L[D][D]DLL[U][U]U(R)[U]URRR[D][D]D[L]L[L]LUUURD[R]R[R]RU
this results in 21 moves before and after the lunch square

Posted by Daniel on 2011-09-15 12:15:11