Is it possible to order a complete set of chess pieces of the same color (8 Pawns, 2 Knights, 2 Bishops, 2 Rook, Queen and King) in such a way that none of them attack each other? If so, how?
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4 Answers
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One could make the argument that the 4 pawns on the top row should be promoted, but other than that, 16 white pieces with none attacking each other, with proper bishop placement.
answered Oct 14, 2014 at 0:08
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1$\begingroup$ If I'm not missing something, you could also move the pawn at f3 and put it at d2 instead, and then flip the board (so the pawns are moving in the other direction) to avoid the promotion problem. $\endgroup$– DoorknobOct 14, 2014 at 0:32
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4$\begingroup$ Bishop covering d2. I'd considered d1 then flipping (only 1 pawn in row 8), but I'd rather have pawns in row 8 than row 1. $\endgroup$ Oct 14, 2014 at 0:41
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$\begingroup$ Gah, I knew I didn't catch something there. According to Wikipedia, though, "There is no restriction placed on the piece that is chosen on promotion," so it should be fine (you could promote the pawn into... a pawn). $\endgroup$– DoorknobOct 14, 2014 at 0:45
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6$\begingroup$ A pawn can be promoted only into a knight, a bishop, a rook, or a queen, so Wikipedia's description is incorrect. (Note however that sometimes chess players use "piece" to mean only those four, and not a pawn or a king. Or sometimes even only knight and bishop.) $\endgroup$– JiKOct 14, 2014 at 12:28
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3$\begingroup$ @JiK: In chess literature, "Piece" always refers to knight, bishop, rook, and queen. "Minor piece" refers to "Only knight and bishop" $\endgroup$ Oct 14, 2014 at 21:38
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I give you the following:
This solution can arise in a regular chess game, where the black king is superfluous. The conditions would still be met if the black king were removed. White needs to make 25 moves (Queenside castle, thanks to h34 in comments) to get into this position, but due to the need of capturing all opposing pieces, a game leading to this position would probably take more turns.
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2$\begingroup$ +1 For finding a solution that does not require unpromoted pawns. $\endgroup$– Briguy37Oct 14, 2014 at 17:14
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$\begingroup$ Excellent. I was trying to find a solution that was possible to achieve in an actual game. I'm now going to stop. $\endgroup$ Oct 14, 2014 at 18:15
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1$\begingroup$ @Ludwik Yes. I've been waiting for my checkmark to disappear. $\endgroup$ Oct 15, 2014 at 20:44
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2$\begingroup$ @JoelRondeau - It is a lot better than the accepted answer because it is a legal position. I have just upvoted it. You only need two more upvotes and you will get a gold badge for it, so don't grumble! :-) Doesn't White only need to make 25 moves, not 26, if he castles queenside? $\endgroup$– h34Jul 15, 2015 at 18:25
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Here is a solution that also maximizes the number of pawns on the board. It also takes into account pawn promotion and the no-pawns-on-first-row rule.
12 Pawns
Ideas used
The area of influence by the rooks is constant wherever they are (2 rows and 2 columns). I placed the bishops and the knights to the side to minimize their area of influence and the rooks on the next columns so the 2 required by the rooks overlap with most of the squares controlled by the knights and bishops.
There are 5 columns remaining at this point and pawns placed in a column render the columns next to them useless. This means the best way to place them is to put them on columns 1, 3 and 5. This leaves the Queen on column 2 or 5.
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1$\begingroup$ This is a nice solution. +1. However, this situation cannot arise from a game, no matter which pawns are scratched, because there is no way the h2 pawn could reach any of the pawn positions. $\endgroup$ Oct 16, 2014 at 9:18
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1$\begingroup$ Nicely spotted. To fix it the King can swap places with either the first or last Pawn on any column. Of course this means that the Pawn next to the new position has to be removed. $\endgroup$– TibosOct 16, 2014 at 12:39
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1$\begingroup$ To fix the h2 issue, flip the board vertically. $\endgroup$– isaacgOct 15, 2016 at 8:59
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$\begingroup$ If you get rid of the a2,a3,a6 and e3 pawns, and swap the king with the e4 pawn. Then it will be possible to add a Black king to a2 and a black pawn to a6. And this position will be not only legal but reachable, due to only needing 14 paws captures to reach. $\endgroup$ Jan 9 at 11:21
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I give you this picture here:
All pieces placed, bishops on opposite colors, and no pawns on the 1st or 8th ranks.
