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Topic: Reverse puzzles and impossible positions (Read 4013 times) |
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leo
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Reverse puzzles and impossible positions
« on: May 24th, 2010, 9:32am » |
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Has it been discussed before?
The puzzle would be a weird position one has to find how it came to be.
Incidentally, are there positions that are impossible to reach even with silly playing? For instance, a melee of interlaced freezings that can't be the result of any move?
I can see one impossible position: 5 rabbits on goal.
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| « Last Edit: May 24th, 2010, 9:33am by leo » |
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ocmiente
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Re: Reverse puzzles and impossible positions
« Reply #1 on: May 24th, 2010, 2:44pm » |
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Regarding impossible positions, I don't know if you could construct impossible positions that did not have something to do with a rabbit reaching the goal line. Although, maybe something having to do with immobilization might work.
Including rabbits reaching goal, the one that came to mind was this:
Code:
+-----------------+
8| . . . . . . . R |
7| . . . . r r r r |
6| . . x . . x . . |
5| . . . . . . . . |
4| . . . . . . . . |
3| . . x . . x . . |
2| . . . . . . . . |
1| . . . . . . . . |
+-----------------+
a b c d e f g h |
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I don't think gold's rabbit could have reached that spot on one turn, and silvers rabbits could not have pushed it there.
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #2 on: May 24th, 2010, 2:55pm » |
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I wonder if there are any positions before the end of the game. I'll try to find one.
Edit: just found one:
I like this one because there are innumerable predecessor positions, but it could not have occurred in any game.
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| « Last Edit: May 24th, 2010, 3:04pm by Isaac Grosof » |
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rbarreira
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Re: Reverse puzzles and impossible positions
« Reply #3 on: May 24th, 2010, 3:04pm » |
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722caasi that's not impossible I think, it's a EMHHDDCC handicap from both sides 
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| « Last Edit: May 24th, 2010, 3:05pm by rbarreira » |
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #4 on: May 24th, 2010, 3:06pm » |
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No, no, no, this is Gold's side of the board. either the gold line forms first, or the silver line does. Once one line has been made, the other one is impossible.
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| « Last Edit: May 24th, 2010, 3:09pm by Isaac Grosof » |
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #5 on: May 24th, 2010, 3:14pm » |
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I'm sorry, that position was possible, because gold pieces could have pushed silver rabbits into place, or vice versa. Here's a better one:
Still innumerable predecessors, but no pesky opposing pieces pushing rabbits around.
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #6 on: May 24th, 2010, 3:39pm » |
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Interesting thought, leo. I know that chess has yielded a reasonable body of "retrograde analysis" puzzles, but I assumed this was mostly to do with some quirky rules like en passant, castling, the prohibition against moving into check, and the obligation to move out of check. I would have guessed that Arimaa would have far fewer positions that are impossible or could only arise in one way, but after a couple of impossible positions by ocmiente and 722caasi, I have to wonder whether I am underestimating the possibilities of retrograde analysis for Arimaa. Perhaps jammed up positions with a lot of freezing restrict the move options enough that one could work backwards.
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| « Last Edit: May 24th, 2010, 3:40pm by Fritzlein » |
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #7 on: May 24th, 2010, 5:20pm » |
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Here's a nice problem:
What did gold just play:
There are only two possibilities. Try to find both.
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| « Last Edit: May 24th, 2010, 5:21pm by Isaac Grosof » |
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FireBorn
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Re: Reverse puzzles and impossible positions
« Reply #8 on: May 24th, 2010, 5:27pm » |
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The rabbit could've started on any of a7, b7, c7, or b6 and gotten to that square, right?
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Sconibulus
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Re: Reverse puzzles and impossible positions
« Reply #9 on: May 24th, 2010, 5:29pm » |
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Or any number of positions involving unfreezing the rabbit on d7 and piece sacrifice
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FireBorn
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Re: Reverse puzzles and impossible positions
« Reply #10 on: May 24th, 2010, 5:33pm » |
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I don't think this one's possible:
Code:
+-----------------+
8| . . . . . . . . |
7| . . . . . . . . |
6| . . x . . x . . |
5| R R r R R r R R |
4| r r R r r R r r |
3| . . x . . x . . |
2| . . . . . . . . |
1| . . . . . . . . |
+-----------------+
a b c d e f g h
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #11 on: May 24th, 2010, 7:31pm » |
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Remember, FireBorn and Sconibulus, the game ends if one side has no rabbits at the end of a turn. Neither of your ideas work, as stated.
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ocmiente
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Re: Reverse puzzles and impossible positions
« Reply #12 on: May 24th, 2010, 7:46pm » |
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That's a good puzzle. Wouldn't have caught that for a long time without the clue.
I think one solution is:
Rd7N re6E Ee7S Ee6E
<EDIT>
And the other must be:
rc7S Eb7e Rd7N Ec7s
But in this case, you don't have to use an elephant to make this work, and the elephant could start from c8 too.
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| « Last Edit: May 24th, 2010, 7:58pm by ocmiente » |
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The_Jeh
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Re: Reverse puzzles and impossible positions
« Reply #13 on: May 24th, 2010, 7:59pm » |
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Ed6w ce6w rf6x Rc7n Ec6x Rc8e
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Isaac Grosof
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Re: Reverse puzzles and impossible positions
« Reply #14 on: May 24th, 2010, 8:14pm » |
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I'm sorry for the inaccuracies. I believe this puzzle fixes all the problems and limits it to one solution.
Is the only solution Rd7n re6e Ed6e Ee6e?
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