## Friday, September 19, 2008

### Intersection: Grid Solitaire Game

You start with an 8-by-8 grid, which is 9-by-9 lines, lightly drawn on
paper.
Start on any corner of the grid.
You draw darker lines along the light lines from vertex to vertex
(vertex = intersection of light lines), alternating drawing horizontal
and vertical lines, not drawing any darker lines where darker lines
You can make your line any length in one direction (up, down, left, or
right) as long as the line goes from the end of the last line to a
vertex of the grid.
No darker lines should coincide, except where the darker lines
intersect (and continue past each other). Your path of connected darker
lines should not even meet itself at any of its corners (meeting at a
single vertex).
You get a point every time an intersection is 'perpendicular' to the
last intersection made (AS the darker lines are being drawn).
(And you get a point for your first intersection.)
By 'perpendicular' intersection, I mean that if your previous
intersection was a horizontal newer dark line crossing a vertical older
dark line, then your current intersection is a vertical newer dark line
crossing a horizontal older dark line, and vice versa.
Your path of connected darker lines starts and stops at the same
corner.
I got 13 points. Can you get 13 points or better?
I also got 14 points by drawing a completely different path. Can you
get 14 points or better?
Example of perpendicular crossings:
(View with fixed-width font.)
.----+...+---+
.....!...!...!
.+---+---+---+
.!...!...!....
.+---+...!....
Example of non-perpendicular crossings:
.----+........
.....!........
.+---+---+....
.!...!...!....
.+---+...!....
.........!....
......---+---+
.........!...!
.........+---+

My 13 point solution:
(Move from * down first.)
*--------+..+-----+......
!........!..!.....!......
!.....+--+--+--+..!......
!.....!..!..!..!..!......
!..+--+--+..!..!..!......
!..!..!.....!..!..!......
!..!..!..+--+--+--+--+...
!..!..!..!..!..!..!..!...
+--+--+--+--+--+--+--+--+
...!..!..!..!..!..!..!..!
...!..!..+--+--+..!..!..!
...!..!.....!.....!..!..!
...!..+-----+-----+..!..!
...!........!........!..!
...+--------+--------+..!
............!...........!
............+-----------+

I will give my 14-point solution now.
(View with fixed-width font.)
Start at * and move upwards first.
+--+..............+--+...
!..!..............!..!...
+--+--+........+--+--+...
...!..!........!..!......
...+--+--+..+--+--+......
......!..!..!..!.........
......+--+--+--+..+--+...
.........!..!.....!..!...
......+--+--+..+--+--+...
......!..!.....!..!......
...+--+--+..+--+--+--+...
...!..!.....!..!..!..!...
+--+--+..+--+--+..+--+--+
!..!.....!..!........!..!
!..+-----+--+........+--+
!........!...............
*--------+...............
Note how different this solution is to the 13-point solution I give
above.

Thanks,
Leroy Quet