Solution by Joey Hwang
Since a marble can't jump over two or more marbles and the marbles can move forward only, if we have the pattern OOB(OBB) with the hole located left(right) to the pattern (Oorange and Bblue), the blue(orange) marble in the pattern will not have any chance to move. So our goal is to prevent generating the above situations. Keeping this in mind, you will find that there is only one way to move the marbles once you finished your first move.
So the only two solutions for the problem are:
4  5, 6  4, 7  6, 5  7, 3  5, 2  3,
4  2, 6  4, 8  6, 9  8, 7  9, 5  7,
3  5, 1  3, 2  1, 4  2, 6  4, 8  6,
7  8, 5  7, 3  5, 4  3, 6  4, 5  6
and
6  5, 4  6, 3  4, 5  3, 7  5, 8  7,
6  8, 4  6, 2  4, 1  2, 3  1, 5  3,
7  5, 9  7, 8  9, 6  8, 4  6, 2  4,
3  2, 5  3, 7  5, 6  7, 4  6, 5  4
Both are done in 24 moves.



Solution by Jensen Lai
if the holes are numbered 19 starting from the left, the sequence is as
follows:
45, 64, 76, 57, 35, 23,
42, 64, 86, 98, 79, 57,
35, 13, 21, 42, 64, 86,
78, 57, 35, 43, 64, 56.
Total 24 moves.
In words the solution is as follows:
If there arises a situation where the marbles are arranged OOBB, where two
oranges are next to two blues, there is a "block" where none of
the marbles can move around the others. To finish the puzzle follow these
steps:
1. move all possible oranges without creating a block.
2. move all possible blues without creating a block.
3. move all possible oranges without creating a block.
4. move all possible blues without creating a block.
etc.
Step 1 makes move 1.
Step 2 makes moves 2 and 3.
Step 3 makes moves 46.
Step 4 makes moves 710.
Step 5 makes moves 1114.
Step 6 makes moves 1518.
Step 7 makes moves 1921.
Step 8 makes moves 22 and 23.
Step 9 makes move 24.
Following this algorithm gives a solution to a puzzle with any number of
marbles on each side of the gap. The least number of moves needed to
complete the puzzle can be given by the formula N=(X+1)squared 1 where X
is the number of marbles on one side of the
gap.



Solution by Michele Ely
The only solution I have come up with takes 24 moves. 14 is the orange marbles, _ is the blank spot and 69 are the blue marbles.
1 2 3 4 _
6 7 8 9
1 2 3 _
4 6 7 8 9
01. (move 4 to the blank spot)
1 2 3
6 4 _ 7 8 9
02. (jump over 4 using 6)
1 2 3
6 4 7 _
8 9
03. (move 7 to the blank spot)
1 2 3
6 _ 7 4
8 9
04. (jump over 7 using 4)
1 2 _
6 3 7
4 8 9
05. (jump over 6 using 3)
1 _ 2
6 3 7
4 8 9
06. (move 2 to the blank spot)
1 6
2 _ 3 7
4 8 9
07. (jump over 2 using 6)
1 6
2 7 3 _
4 8 9
08. (jump over 3 using 7)
1 6
2 7 3
8 4 _ 9
09. (jump over 4 using 8)
1 6
2 7 3
8 4 9 _
10. (move 9 to the blank spot)
1 6
2 7 3
8 _ 9 4
11. (jump over 9 using 4)
1 6
2 7 _ 8
3 9 4
12. (jump over 8 using 3)
1 6 _
7 2 8
3 9 4
13. (jump over 7 using 2)
_ 6 1
7 2 8
3 9 4
14. (jump over 6 using 1)
6 _ 1
7 2 8
3 9 4
15. (move 6 to the blank spot)
6 7 1 _
2 8 3
9 4
16. (jump over 1 using 7)
6 7 1
8 2 _ 3
9 4
17. (jump over 2 using 8)
6 7 1
8 2 9
3 _ 4
18. (jump over 3 using 9)
6 7 1
8 2 9 _
3 4
19. (move 3 to the blank spot)
6 7 1
8 _ 9 2 3 4
20. (jump over 9 using 2)
6 7 _
8 1 9
2 3 4
21. (jump over 8 using 1)
6 7 8 _
1 9 2 3 4
22. (move 8 to the blank spot)
6 7 8 9
1 _ 2 3 4
23. (jump over 1 using 9)
6 7 8 9 _
1 2 3 4
24. (move 1 to the blank spot)



Solution by John Birch
Nifty puzzle ! There are some interesting mathematics in it.
Thanks for the clean & handy Flash implementation.

... I solved it intuitively, in 24 moves, and found that backward it was
move
#
123456789 hole#
24 bbbbxoooo
23 bbbboxooo
22 bbbxobooo
21 bbxbobooo
20 bbobxbooo
19 bbobobxoo
18 bboboboxo
17 bboboxobo
16 bboxobobo
15 bxobobobo
14 xbobobobo
13 obxbobobo
12 obobxbobo
11 obobobxbo
10 obobobobx
9 oboboboxb
8 oboboxobb
7 oboxobobb
6 oxobobobb
5 ooxbobobb
4 ooobxbobb
3 ooobobxbb
2 oooboxbbb
1 oooxobbbb
0 ooooxbbbb
123456789 hole#
Most simply put, I can specify the piece to be moved, in the move order :
467532468975312468753465
Since there is always only 1 hole to receive that piece, no other punctuation nor digits are needed by anyone, to perform the moves.
This solution is topologically identical to three other solutions, since the holes & the move numbers (order) can each be reversed without changing the nature of the solution.
As far as I can see, this is the only solution, which implies that rule 6 is unneeded.
Here are the rules to solve the puzzle: { Only rules 2, 3, & 4 are necessary. }

Move the Blue marbles to the left and the Orange  to the right, again leaving an empty hole in the middle.
1. The marbles move (or jump) one at a time, into the empty hole. {unneeded rule?}
2. The marbles move toward the opposing side only.
(Blue  to the left, Orange  to the right), and never backward. {Colors are unnecessary, if you follow the rules, but make completion easier to verify.}
3. Any marble can move one step into the empty hole next to it.
4. A marble can jump over only the marble next to it, landing on the empty hole {immediately} beyond it.
5. They can't jump over two or more marbles. {except on separate moves. see rule #4}
6. The puzzle should be solved with a minimum number of moves.
{This might be a goal, but is not a usable rule.
Is it possible to solve with other than 24 moves ?}

In the format you requested the solution was
45, 64, 76, 57, 35, 23,
42, 64, 86, 98, 79, 57,
35, 13, 21, 42, 64, 86,
78, 57, 35, 43, 64, 56
24 moves



Solution by Ian Pedder
The puzzle can be solved in 24 moves as follows:
4  5
6  4
7  6
5  7
3  5
2  3
4  2
6  4
8  6
9  8
7  9
5  7
3  5
1  3
2  1
4  2
6  4
8  6
7  8
5  7
3  5
4  3
6  4
5  6
It seems that for puzzles of this sort, with N pieces of each color then the minimum number of moves required is N * (N + 2).
Thus with N = 4 in this case requires 4 * 6 = 24 moves.



Solution by Emrah Baskaya
Thanks for your great puzzles page.
It seems there can only be two solutions, the one I am sending and its mirror. I am extremely curious if there can be other ways to solve it (other than the mirror.) I'll go as far as saying nobody can solve it with more than 24 moves. The puzzle seems pretty much fixed and the only way is using "avoid moves leading to two marbles of same color next to
each other in front of opposite color" pattern...
...here goes the solution:
65,46,34,53,75,87,
68,46,24,12,31,53,
75,97,89,68,46,24,
32,53,75,67,46,54
Done
24 moves.
And the mirror of the solution starts of course with:
45, and goes on.



Solution by Brian M. Dailey
I had a bunch of fun with your oxbow puzzle.
Here is the solution I came up with:
number of moves 24,
45,64,76,57,35,23,
42,64,86,98,79,57,
35,13,21,42,64,86,
78,57,35,43,64,56:
it works backwards too:
65,46...
Thanks for the fun
PS.
The solutions can be written shorter, because there is only one open space on a board at any time. As long as you know the first move the rest the second numbers should match the first numbers. eg. solution 24 moves:
45,6,7,5,3,2,
4,6,8,9,7,5,
3,1,2,4,6,8,
7,5,3,4,6,5



Solution by Nigel Wilson
45,64,76,57,35,23,
42,64,86,98,79,57,
35,13,21,42,64,86,
78,57,35,43,64,56
24 moves
The secret is to avoid 2 consecutive of the same colour.



Solution by Carol
It took me 24 moves to win the game. I played it 5 times and won, this is a supper game!!!!!!
Thank you



Solution by Sue Hinman
Thanks for a fun puzzle and a great website. My students had a great time figuring this out! Though difficult at first, once they figured out the secret, they could solve it quickly. It was a good confidence builder. Other than a mirror image solution, we can't imagine there's any other way to solve this, so we'll be interested to see if there are other solutions or not. Thank you again!
45
64
76
57
35
23
42
64
86
98
79
57
35
13
21
42
64
86
78
57
35
43
64
56
24 moves



Solution by Russell Baum
Thanks for the great site which I have just come across...
The solution to mini contest 20 is as follows:
This is actually very straight forward since the balls cannot move backwards. Consequently at every stage there are very few legal moves available and incorrect moves are easy to spot before they become
problems. Obviously the puzzle can be solved moving orange first or blue first with the same pattern of moves. Starting the puzzle with a jump is no good as it then creates a buffer that stops the second colour from moving. The first move therefore is the first ball into the middle. Moving the same colour again, either by a single move or a jump creates another buffer so the second move must be a jump by the first ball in the second colour. Using the same logic from then on keeping colours separate provides the solution below.
45, 64, 76, 57, 35, 23,
42, 64, 86, 98, 79, 57,
35, 13, 21, 42, 64, 86,
78, 57, 35, 43, 64, 56
24 moves.



Solution by David Atkinson
I had a go at your Oxbow Puzzle. I used a pen and paper to write down my moves, and marked where there was more than one move that wouldn't result in getting stuck, so I could easily go back and try the other move. I hope that isn't considered cheating :) Anyway here is the result I got:
I solved it in 24 moves.
65, 46, 34, 53, 75, 87,
68, 46, 24, 12, 31, 53,
75, 97, 89, 68, 46, 24,
32, 53, 75, 67, 46, 54.
After solving it with pen & paper, I then wrote a C program to see if there were any other ways of solving it. There is 1 other way, which appears to be by starting with the opposite move ie. 45, 64, 76 (which incidentally is what you get if you read my solution backwards).
Thanks for the puzzle!






Oxbow Puzzle
(solution)
There are just two symmetrical solutions to this puzzle; both count 24 moves.
Some of your correct solutions with interesting
comments are shown below.
Also there were some great comments and suggestions regarding the set of
rules to the Oxbow Puzzle and its solution's notation. Thanks a lot for
them! We'd only like to point out that our main goal
was to save the true puzzle "smell" of this nice puzzle gem. So
we've just used the rules accompanying the real old sample of this puzzle,
and tried to presented them as clear as possible. 