Knights Move: A Chess Game Puzzle

) It shows a 3x3 chessboard with white knights on (row 1, column 1) and ) (3,1); and black knights on (1,3) and (3,3). Instructions are 'Using ) only Knight's moves; exchange the position of the black and white pieces ) in seven moves.' ) ) I've worked at it and can get the moves completed in 8 moves, but not seven.

Given this description, I don't see a solution in 8 moves. Therefore, I must have misunderstood the puzzle description. Is the following correct ?

- With a knight's move from any of the four corner squares, the only two squares you can reach are the two edge squares next to the opposite corner square. - From any of the four edge squares, the only two squares you can reach are the two corner squares next to the opposite edge square. The center square cannot be reached from any other square. - To get a piece from a corner square to another corner square requires at least two moves.

If not, could you describe the puzzle more clearly ?

Hello Willem;

All of your statements are correct. I think you understand the puzzle clearly. Unfortunately, I believe there's some 'trick' to this that allows it to be solved.

Side comments on the game include: The Diabolical, The Ingenious, The Puzzle No Mortal can Solve!

My solution, in 8 moves, is to move Black Knight (1,1) to (3,2); White Knight (1,3) to (3,2)...Yep, stack the white on top of the black (after all, they're flat tiles!). Then move White Knight (3,2) to (1,1), Black Knight (3,2) to (1,3) This switches 2 knights in 4 moves. Do the same to the other 2 knights: Black Knight at (3,1) goes to (1,2) then (3,3). White Knight at (3,3) goes to (1,2) then (3,1). But this is still 8 moves, and the puzzles says 'exchange the position of the black and white npieces in seven moves.' So I'm still taking 1 too many moves.

Jay Schindler

I believe the trick to this puzzle is that it says that No Mortal can solve it. As far as I know only mortal's have attempted this puzzle, and most likely have failed. Perhaps if there is a nonmortal, in this group, they could perhaps solve it =)

Also, I don't think you are allowed to stack the pieces, because that would violate the rule that 'only knights moves are allowed' although i suppose it depends on how you interpret the wording.

Well, counting moves in the ordinary way, it takes 16 moves. However, if you count all consecutive moves by a single piece as one, then I get seven.

Explanation below:

Take the grid:

A1 B C1

D E F

G2 H I2

1's are wh. knights, 2's are black knights.

Call two squares connected if it is possible to move between them with one knight's move.

Now, A is connected to F and H; B is connected to G and I, ...

1 1 2 2

) All of your statements are correct. I think you understand the puzzle ) clearly. Unfortunately, I believe there's some 'trick' to this that ) allows it to be solved. ) ) Side comments on the game include: The Diabolical, The Ingenious, The ) Puzzle No Mortal can Solve! ) ) My solution, in 8 moves, is to move Black Knight (1,1) to (3,2); White ) Knight (1,3) to (3,2)...Yep, stack the white on top of the black (after ) all, they're flat tiles!). Then move White Knight (3,2) to (1,1), Black ) Knight (3,2) to (1,3) This switches 2 knights in 4 moves. Do the same ) to the other 2 knights: Black Knight at (3,1) goes to (1,2) then (3,3). ) White Knight at (3,3) goes to (1,2) then (3,1). But this is still 8 ) moves, and the puzzles says 'exchange the position of the black and ) white npieces in seven moves.' So I'm still taking 1 too many moves.

Thought as much. You can easily see that there are only two possible series of moves by one piece. This series will visit the corner squares after every two steps, either in clockwise or counterclockwise order.

So, if you allow stacking, you just have to interleave the moves so that the stacks come out 'right'.

You can simply see that the solution needs 8 moves.

I'll try to list as many 'givens' as possible, that are needed to prove that 8 moves are required.

Given: - A knight's move means going from (a,b) to (a +/- 2, b +/- 1) or to (a +/- 1, b +/- 2) - The corners have coordinates (1,1), (1,3), (3,1), (3,3) - The edges have coordinates (1,2), (2,1), (2,3), (3,2) - The centers has coordinates (2,2) - No other squares exist You can deduce that a knight's move is either from a corner to an edge or vice versa.

Given: - Each knight starts on a corner - Each knight ends on a corner - No knight ends on the corner it starts on - A knight's move is either from a corner to an edge or vice versa - A 'move' is one single knight's move - There are four knights You can deduce that you need two moves to get a knight to its target, and therefore eight moves to get all four to their targets.

What you need to do is break one of these 'givens' and label that a 'trick' (instead of calling it cheating)

Possibility: - A 'move' is not one single knight's move, but a series of knight's moves by one knight (or one knight's move by multiple knights)

A knight always moves from black to white square, or vice versa. Initially all knights are on same color. To bring all of them back on the same color would require an even number of moves; hence there cannot be a solution in seven moves.

Cheers!

- Risto -