solve this 3 x 2 sliding block puzzle in fewest moves.

Posted on 2013-01-07
Last Modified: 2013-01-08
Given the following sliding blocks:  (b = a blank space to move blocks)

1   B
5   4
3   6

Re-arrange the 5 and the 3 in the fewest moves.  so that it looks like this:

1   B
3   4
5   6

Post the solution as 1R, 5U  (i.e. move the 1 block right.  Move the 5 block Up, etc.)
Would love someone to explain to me the logic in solving this.  I'm stuck!
Question by:arthurh88
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LVL 84

Expert Comment

ID: 38753739
Not possible.
The requested re-arrangement requires an odd number of swaps,
But getting B back to its starting position requires an even number of swaps.

Author Comment

ID: 38753820
is it possible then to get
B   1
3    4
5    6


The key for me is the 3, 4, 5, 6 in the right positions
LVL 84

Expert Comment

ID: 38753854
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Author Comment

ID: 38753861
ok can you please help me understand why?   how do you know the even/odd thing?   is there an explanation that might make sense to a laymen?
LVL 84

Accepted Solution

ozo earned 500 total points
ID: 38754252

Author Comment

ID: 38755680
wow thanks.  i searched wikipedia for "sliding block puzzle" but didn't know what it was really called.

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