# Gone ortho-flogging

Well played, Scratchy, you just took 8 shots on Hole 9 of Puzzlington Municipal Ortho-flog Course!

         As presented                         As flogged (solved) by you
-----------------------------           ------------------------------------

Cup                 <pre>
(begin)                        7 1 2 3 4 5 6 7 8
|                           6               1
5           4 3 2 1 2
4           1   3   1
Hole 9        . . .(0)                          3           2   4 . 1(0)
.     .                           2           3   5     .
3 left        .     .                           1           4   6     .
5 down        .     .                           6 5 4 3 2 1 5   7     .
.     .                                           8     .
[ ]. . o o                                        [9]. . o o
</pre>

|      |                 SCORE = 8 shots
Tee   Trees
(end) (avoid)         (periods . are grid marks for reference)


What the “ortho-flog”?   Just backwardsgolf,” of course, on an orthogonal grid.  At each hole:

• Begin at the (0) cup, end at the [ ] tee.

• Make a path of consecutive “shots.”  The path may overlap itself but not o trees.

• The more shots the better.  For equal shot counts, longer shots are favored.

• Shots alternate between up-or-down (1 step = 1 line) and left-or-right (1 step = 2 character spaces), starting in any of those directions.

• Each successive shot is longer than the last, but never longer than 9.  (In the order flogged above, shots at Hole 9 are 1 left, 2 up, 4 left, 5 down, 6 left, 7 up, 8 right, 9 down.)

• Surround your solution with <pre> and </pre> to produce even typewriter-like spacing.

Try for the greatest total shot count over all 9 holes.  Please use , though, as this course is not meant to accommodate byte supremacism.  Here is your scorecard so far.

     ________________________________________________________________________
|          |       |     |     |     |     |     |     |     |     |     |
|   SCORE  |   8   |     |     |     |     |     |     |     |     |  8  |
|          |_______|_____|_____|_____|_____|_____|_____|_____|_____|_____|
|          |       |     |     |     |     |     |     |     |     |1 2  |
|   Shot   |       |     |     |     |     |     |     |     |     |4 5 6|
|  lengths |   42  |     |     |     |     |     |     |     |     |7 8 9|
|          |_______|_____|_____|_____|_____|_____|_____|_____|_____|_____|
|            Total    1     2     3     4     5     6     7     8     9  |
|                                                                        |
|If total scores are equal, the largest total of shot lengths is favored.|
| If length totals are also equal, square each shot length and re-total. |
|   Repeat with cubes and so on as long as those totals remain equal.    |
|________________________________________________________________________|


                                                                            .
Hole 8                          . . . . .(0)                            .
.         .                             .
5 left                        o .         .                             .
4 down                          .         .                             .
[ ]        .                             .
. . . . . .                             .
o                                 .

                                                                            .
Hole 7                            . . . .(0)                            .
.       .                             .
5 left                            . o     .                             .
4 down                            .       .                             .
[ ].       .                             .
. . . . .                             .
o                             .

                                            o                               .
Hole 6                            . . . . .                             .
.      (0)                            .
5 left                            .       .                             .
4 down                            .       .                             .
.       .                             .
[ ].       .                             .
. . . . .                             .
o                                 .

                          . . . . . o . o . o . o . . . .                   .
Hole 5                .     o                   o   .                   .
.                           o .                   .
9 left                . o   . . . . o . o . . .     .                   .
8 down                .     .   o           o .     o                   .
o     . o               .     .                   .
.     .     . o o .     o     o                   .
o     o     .    (0)    .     .                   .
.     .     o     . o o .     o                   .
o     o     .                 .                   .
.     .     o               o .                   .
o     o     . . o . o . o . . .                   .
.     .                                           .
o     . o                                         .
.     . . . o . o . o . o . o . o . o             .
[ ]                                                .
.

                                                                            .
Hole 4              . . . . . . . . . . . . . . . . . . .(0)            .
.                                     .             .
19 left              .                                     .             .
7 down              .                                     .             .
.                                     .             .
.                                     .             .
.                                     .             .
[ ]. . . . . . . . . . . . . . . . . . .             .
.

                                                  o                         .
Hole 3                        . . . . . . . .(0)                        .
.               .                         .
8 left                        .               .                         .
5 down                        .               .                         .
.               .                         .
[ ]. . . . . . . .                         .
.

                                              o                             .
Hole 2                        . . . . . . . . .                         .
.              (0)                        .
8 left                        .               . o                       .
3 down                        .               .                         .
[ ]. . . . . . . .                         .
.

                                                  o                         .
Hole 1                        o o . . . . . . .                         .
.             .                         .
1 down                          .  (0)        .                         .
.  [ ]  o o   .                         .
o . . . . . . . .                         .
o                                       .


Any solution should begin with a summary scorecard, copied from above. As always, some analysis is expected.

• A tee in one is only possible on Hole 1, though it would be the worst possible score
– humn
Commented Sep 21, 2017 at 21:30
• @GarethMcCaughan Underneath the solved hole: "(periods . are grid marks for reference)" Commented Sep 21, 2017 at 22:31
• At most one shot of length 9, and none is okay too, @DqwertyC, the puzzle statement has been revised. Thank you for pointing out an ambiguity.
– humn
Commented Sep 21, 2017 at 22:45
• When your path crosses itself, does it have to be on the same number? Commented Nov 4, 2017 at 1:11
• Doesn't have to be the same number on crossings, @boboquack, sorry about the false artifact.
– humn
Commented Nov 4, 2017 at 1:13

## Warning: I have answers for everything, without spoilers blocks

After much pen-and-paper case bashing (like, 10 pages worth - I am not going to reproduce it here) this is what I came up with:

     ________________________________________________________________________
|          |       |     |     |     |     |     |     |     |     |     |
|   SCORE  |  60   |  1  |  5  |  8  |  8  |  2  |  8  |  9  |  9  |  8  |
|          |_______|_____|_____|_____|_____|_____|_____|_____|_____|_____|
|          |       |1    |1   3|1 2 3|1 2  |     |1   3|1 2 3|1 2 3|1 2  |
|   Shot   |       |     |4 5  |4 5 6|4 5 6|     |4 5 6|4 5 6|4 5 6|4 5 6|
|  lengths |   ??  |     |  8  |7   9|7 8 9|  8 9|7 8 9|7 8 9|7 8 9|7 8 9|
|          |_______|_____|_____|_____|_____|_____|_____|_____|_____|_____|
|            Total    1     2     3     4     5     6     7     8     9  |
|                                                                        |
|If total scores are equal, the largest total of shot lengths is favored.|
| If length totals are also equal, square each shot length and re-total. |
|   Repeat with cubes and so on as long as those totals remain equal.    |
|________________________________________________________________________|



                                         6 1 2 3 4 5 6 7                     .
5             1                     .
4   2 1 2 3   2                     .
3   1     1   3                     .
Hole 8                          . . 2 . 1(0)  2   4                     .
.   1     .   3   5                     .
5 left                        o .   5 4 3 2 1 4   6                     .
4 down                          .         .       7                     .
[9]8 7 6 5 4 3 2 1 8                     .
. . . . . .                             .
o                                 .

                                                                            .
Hole 7                            . . . .(0)1                           .
.       . 1                           .
5 left                            . o 3 2 1 2                           .
4 down                            .   1   .                             .
8 1 2 3 4 5 6 7 8[9].   2   .                             .
7                   . . 3 . .                             .
6             5 4 3 2 1 4   o                             .
5             1                                           .
4             2                                           .
3             3                                           .
2             4                                           .
1             5                                           .
7 6 5 4 3 2 1 6                                           .

                                    8 7 6 5 4 3 2 1 7                       .
1               6                       .
2   4 3 2 1 3   5                       .
3   1   o   2   4                       .
Hole 6                          4 . 2 . . . 1   3                       .
5 . 3    (0)1   2                       .
5 left                          6 . 4     .     1                       .
4 down                          7 . 5 1 2 3 4 5 6                       .
8 .       .                             .
[9].       .                             .
. . . . .                             .
o                                 .

                          . . . . . o . o . o . o . . . .                   .
Hole 5                .     o                   o   .                   .
.                           o .                   .
9 left                . o   . . . . o . o . . .     .                   .
8 down                .     .   o           o .     o                   .
o     . o               .     .                   .
.     .     . o o .     o     o                   .
o     o     .    (0)    .     .                   .
.     .     o     1 o o .     o                   .
o     o     .     2           .                   .
.     .     o     3         o .                   .
o     o     . . o 4 o . o . . .                   .
.     .           5                               .
o     . o         6                               .
.     . . . o . o 7 o . o . o . o . o             .
[9]8 7 6 5 4 3 2 1 8                               .
.

                                                                            .
7 6 5 4 3 2 1 6                   .
Hole 4              . . . . . . . . . 1 . . . . . . 5 . .(0)            .
.                 2             4     1 1 2         .
19 left              .                 3             3     .   1         .
7 down              .                 4             2     .   2         .
.                 5             1     .   3         .
.                 6             5 4 3 2 1 4         .
.                 7                   .             .
[9]8 7 6 5 4 3 2 1 8 . . . . . . . . . .             .
.

                                  7 6 5 4 3 2 1 6                           .
1             5                           .
2             4   2 1 2 3                 .
3             3 o 1     1                 .
Hole 3                        4 . . . . . . 2(0)1     2                 .
5             1 .       3                 .
8 left                        6             5 4 3 2 1 4                 .
5 down                        7               .                         .
8               .                         .
[9]. . . . . . . .                         .
.

                                  5 4 3 2 1 4                               .
1         3                               .
2         2                               .
3         1 o                             .
Hole 2                        4 . . . . 3 2 1 1                         .
5              (0)                        .
8 left                        6               . o                       .
3 down                        7               .                         .
[8]. . . . . . . .                         .
.

                                                  o                         .
Hole 1                        o o . . . . . . .                         .
.             .                         .
1 down                          .  (0)        .                         .
.  [1]  o o   .                         .
o . . . . . . . .                         .
o                                       .


I believe I have proved uniqueness for most of the holes, but am not sure about that.

## Hole 8, Score 9

                                         6 1 2 3 4 5 6 7                      .
5             1                     .
4   2 1 2 3   2                     .
3   1     1   3                     .
Hole 8                          . . 2 . 1(0)  2   4                     .
.   1     .   3   5                     .
5 left                        o .   5 4 3 2 1 4   6                     .
4 down                          .         .       7                     .
[9]8 7 6 5 4 3 2 1 8                     .
. . . . . .                             .
o                                 .
LEFT | +1  -3  +5  -7  +9 | +5
DOWN |   -2  +4  -6  +8   | +4

I think this is the only possible answer for hole 8 with score 9.

Hole 7 and hole 6 are also 5 steps left and 4 steps down, but the same route is blocked by a tree. So some numbers should be skipped.

# Partial answer - Holes 7, 6 and 3

## Hole 7 - score 9

                                                                            .
Hole 7                            . . . .(0)1                           .
.       . 1                           .
5 left                            . o 3 2 1 2                           .
4 down                            .   1   .                             .
8 1 2 3 4 5 6 7 8[9].   2   .                             .
7                   . . 3 . .                             .
6             5 4 3 2 1 4   o                             .
5             1
4             2
3             3
2             4
1             5
7 6 5 4 3 2 1 6


## Hole 6 - score 8

                                    8 7 6 5 4 3 2 1 7
1               6
2   4 3 2 1 3   5
3   1   o   2   4                       .
Hole 6                          4 . 2 . . . 1   3                       .
5 . 3    (0)1   2                       .
5 left                          6 . 4     .     1                       .
4 down                          7 . 5 1 2 3 4 5 6                       .
8 .       .                             .
[9].       .                             .
. . . . .                             .
o                                 .


## Hole 3 - score 7

                                      6 1 2 3 4 5 6 7
5             1
4           o 2                       .
Hole 3                        . . 3 . . . 2 1(0)3                       .
.   2       1   . 4                       .
8 left                        .   1       2   . 5                       .
5 down                        .   4 3 2 1 3   . 6                       .
.               . 7                       .
[9]8 7 6 5 4 3 2 1 8                       .
.


NB: I believe these are optimal but I might have missed something.