# No More Kings puzzle

Inspired by the game No More Kings

Rules:

• You start as the black piece.
• Your goal is to capture every piece on the board.
• The king must be the last piece captured.
• Captured pieces are used as the next move.

Example: If a rook captures a bishop, play continues from the position of the bishop with piece movement of the bishop.

Solution:

I didn't have a method. It happened to be the first path I tried.

• Since it was the first path I tried, I wonder if there are more solutions. This would be a cool puzzle type to refine and use the moves to draw a picture of something. – Forklift May 24 '17 at 13:58
• This is the cleanest demonstration of the solution so far. In regards to there being more solutions, I figured out the same path by realising only 6 could capture 7. Using retrograde analysis, there was only one piece that could capture 6, etc... So it does seem to be a unique solution. – Reti43 May 24 '17 at 16:59
• 9 and 10 can only capture each other, so one of them must be the final move. Since 8 can only capture 9, the final three moves therefore must be as above. From there, it's straightforward to trace backward with only one possible move available at each step. – user3294068 May 30 '17 at 15:04

There's nothing wrong with Forklift's solution, but here's how to be a bit more methodical. First of all

the possible captures form a directed graph (with a bit of subtlety when pieces' possible paths pass through other pieces that may or may not have been captured by the relevant point):

Now there are some captures we can identify with confidence.

The Ne7 can be captured only by the Nc6, after which the only thing it can do is to capture the Rc8. And the Pa3 can only capture the king. If the Rc8 is captured by the Ne7 then it isn't captured by the Bg4, whose only other available capture is the Bf3; it then has nothing to do but capture the Nc6. What captures the Bg4? The only thing that can is the Ne5, so we know how everything begins: so we have the sequence Ne5-Bg4-Bf3-Nc6-Ne7-Rc8. The Rc8 can now capture the Bh8 and nothing else can, and then the Bh8 has nothing to do but capture the Ra1. So Ne5-Bg4-Bf3-Nc6-Ne7-Rc8-Bh8-Ra1.

And now

it's obvious that the only way to finish is Ra1-Bc1-Pa3-Kb4.

• I knew I should have used red arrows. Way better. – Forklift May 24 '17 at 15:02
• It's the artistry and sheer geometrical precision in my presentation that really lifts it to the highest level, I think. – Gareth McCaughan May 24 '17 at 15:08
• "bit more methodical" I guess unintelligible mass of red lines and arrows is a bit more methodical. @Forklift Freehand red circles would be even better. – jpmc26 May 24 '17 at 22:47
• lol. Sorry. I meant that comment to be completely in jest, but I don't think I quite got that tone across. – jpmc26 May 25 '17 at 0:32
• @Forklift: The key is freehand red arrows.    :-)   ⁠ – Peregrine Rook Jul 9 '17 at 22:43

Answer using one non-capturing move (pawns aren't pieces in Chess):

... xB (KN6)
... xB
... xR
... xB
... xR
... xB
... -KN4
... xN
... xN
... xK


If you can't make free moes I'm absolutely certain the given answer is the only one.

• Pawns aren't pieces in chess? What would you call them? – David Starkey May 24 '17 at 17:10
• @DavidStarkey: Pawns are pawns. Pieces are everything else but the kings. – Joshua May 24 '17 at 17:27

The exists only one unique solution to this problem. Here is how to solve it-

Draw an arrow moving away from every piece, towards all pieces that the piece can kill. After you are done drawing a the complete network of arrows, connect them in head to tail basis, starting from the knight and ending at the king. There​ will be clues within on how to proceed, like the pawn can kill only the king, so it must kill the king, etc.