Possible to figure out whose go it is in checkers game, based purely on the position of pieces on the board? I came across a checkers board in my house with an unfinished game on it which made me wonder if it possible, just by looking at the positions of the pieces on the board, whose go it is next. For example, this is impossible in chess (I.e. There are plenty of positions which come to mind where it is impossible to determine who goes next.)I was wondering if it is the same for checkers. I feel that it should be determinable but I'm not sure. I tried to prove it by numbering the rows of the checkers board and assigning values to each piece based on the row the piece is in, and created a semi-successful system where different positions could be described as even or odd, each indicating a different player to move next. That said, the system failed to work in some situations (capturing wasn't properly accounted for). Of course, if someone can come up with a counter example, that would solve the problem. Does anyone have any ideas for how to solve a question like this? Many thanks!
 A: I have a counterexample.

suppose both sides have that sort of situation somewhere on the board and it's red's move. Then red can make a double jump followed by 4 moves to take both blues and get back (5 moves) or two single jumps followed by 4 moves to get to the same position in 6 moves.
If blue chooses to do it in 5 moves, then depending on whether red does it in 5 or 6 moves, it could either be blue's or red's move when they're both back in their original positions and you have no way to tell.
EDIT: As @bof pointed out, my initial intuition was incorrect, and it's impossible even without kings or double jumps.
A: The game starts with the 12 white men on the black squares of the bottom three rows, and the 12 black men on the black squares of the top three rows. White is moving up the board, Black is moving down the board; as usual in checkers, Black moves first. I will use chess notation instead of checkers notation for the squares, because I think more people are familiar with that.
Note that the following two games arrive at the same position, but with different players on the move:
$\ \ $ Black White
1. h6-g5 c3-d4
2. g7-h6 a3-b4
3. h8-g7 b4-c5
4. d6-b4 g3-h4
5. b4-a3 h2-g3
$\ \ $ Black White
1. d6-c5 a3-b4
2. c5-a3 c3-d4
3. h6-g5 g3-h4
4. g7-h6 h2-g3
5. h8-g7
