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This puzzle is part of the Fortnightly Topic Challenge - "Unconventional Tag Fusion".

Last week I found out that Puzzle Prime Co. have invented new type of puzzle - Rubik's Chess. The goal is simple - you get a scrambled cube with various chess pieces on its sides, and you must unscramble it so that on each side there is one mated king (K), assuming the kings can not capture the neighboring pieces (Queens, Rooks, Bishops, kNights). Puzzle Prime was offering cubes of varying difficulties, ranging from A-rank, all the way to Z-rank. I decided to go with something medium, so purchased a "P" and received it few days later in my mailbox.

enter image description here I am usually good with this type of puzzles, but I spent my entire weekend trying to solve this one without any success. I even started wondering if it can be actually solved, so decided to share it with you and see if someone can help me figure that out.

I couldn't create a proper 3D model of the puzzle, but fortunately @Sleafar managed to draw a wonderful diagram showing all faces of the cube when seen from the top and the bottom:

enter image description here

Remark: The orientations of the pieces are irrelevant of the final solution, i.e. they don't need to be consistent on each side.

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  • $\begingroup$ Wow, it's simply amazing :D $\endgroup$ – ABcDexter Nov 4 '16 at 8:05
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    $\begingroup$ To clarify, each face is considered a separate 3x3 board that is not attacked by the pieces on the other faces? I.e. the attacking range of a piece does not go past the edges of a face onto the adjacent face? $\endgroup$ – Jaap Scherphuis Nov 4 '16 at 11:56
  • $\begingroup$ Nice idea, Artur! $\endgroup$ – dcfyj Nov 4 '16 at 12:07
  • $\begingroup$ @Sleafar, not sure if you read my edited comment, but if you can add a non-colored version of your first picture with white background to the problem formulation, it will be great. Looked really nice. $\endgroup$ – Puzzle Prime Nov 4 '16 at 22:40
  • $\begingroup$ Here is the image. I'll try to mate the kings tomorrow. $\endgroup$ – Sleafar Nov 4 '16 at 22:46
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I'm afraid the reason you couldn't solve this puzzle is: there is simply no solution (as clarified by the OP, this is a P-rank cube).

Let's analyze the cube. There are 6 kings (of course) and 13 other pieces. None of these pieces can mate a king on its own, which means we will have 5 faces with 2 mating pieces, and 1 face with 3 mating pieces.

I used my favorite, proven for decades, method to solve the cube: break the whole cube apart and put the pieces together placed correctly. Therefore you won't see move lists this time.

Let's analyze the cube in the picture below. There are 2 center kings. They can be attacked only by 2 of the available pieces: the corner queen and the corner bishop. They are marked orange and yellow in the picture below, together with the corresponding kings. Because all center pieces are symmetric, it doesn't matter which of both pieces attacks which king. There is also a rook (marked green) on the corner piece containing the queen. It must be paired with one of the other center pieces, and this works only with another rook (marked green as well). Combining the corner rook with a center bishop would make it impossible to mate a king on that face.

enter image description here

Now, let's look at the next image. To mate the kings on the orange and yellow face, we need to control and/or block the red marked squares. In the orange case, it's only possible with a border bishop. This border bishop has another one attached to it (marked blue). It needs to be combined with a center bishop (marked blue as well) to be able to mate a king on that face (it wouldn't work with a center rook). Controlling all red squares on the yellow face, requires at least 2 pieces (now we know the face with 3 mating pieces). To be more specific, it works only with the 2 corner knights.

enter image description here

Now, let's look at the final image. There is a corner knight (marked purple) on the same cube piece as the yellow corner bishop. It has to be paired with a center bishop (marked purple as well) to be able to mate a king at all (doesn't work with center rook). BUT there would need to be a king on the red marked square which is simply impossible, because this is the queen/rook corner piece which we placed at the beginning.

enter image description here

The placement of all marked pieces was forced, and there is no way to fix the cube in the image above using the remaining pieces, which means: there is no solution.

A simple change to make this solvable would be to move either the king or the knight on the purple face from the lower to the upper row. All other faces are already correct.

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  • $\begingroup$ Sleafar, I'm sorry - maybe there is some misunderstanding? Each king must be mated, not checked. Also, can you add a non-colored version of your first image in the problem formulation? It looks great. $\endgroup$ – Puzzle Prime Nov 4 '16 at 22:38
  • $\begingroup$ @ArturKirkoryan I think I fixed the "solution" now. $\endgroup$ – Sleafar Nov 5 '16 at 10:29
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    $\begingroup$ It looks right, and the explanations are very clear. I also just realized that this P-rank cube is probably nothing else but a prank. Thank you:) $\endgroup$ – Puzzle Prime Nov 5 '16 at 12:47
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I'm not at all certain this is correct, as I'm terrible at Rubik's Cubes, but I think I may have found a solution.

     _ _
    |Q  |
    | K |
 _ _|_B_|_ _ _ _
|R K|KB | K |N  |
| R | B | R | B |
|_ _|_ _|_N_|__K|
    |B N|
    | K |
    |N__|

I started by

Counting the Edge and Corner pieces of each type, then working out a checkmate for each face using them.

Then I looked at

Which pieces were shared, and found that the overlaps were Edge BB, Corner KN_, Corner KK_, Corner QR_

I then

Rearranged the Checkmates I'd found to match the overlaps, and hoped for the best.

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    $\begingroup$ Your solution shows a different cube. In the original puzzle there is only one corner piece with a bishop, and it has a knight on one of the other squares. In your solution both other squares on the corner piece with the bishop are empty, and the knight is on a different corner piece. $\endgroup$ – Sleafar Nov 5 '16 at 7:29

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