# Find the color of the chess pieces

The colors of the pieces in the diagram is unknown. The diagram can be obtained from a real game. One needs to find the color of each piece: Black or White.

I do not know the full solution.

It is easy to find the colors of most of the pieces:

1. The kings should not be checkmated by pawns (otherwise what was the previous move?), so the upper one is white.
2. The knight on g4 gives a checkmate to some king, so this was the last move.
3. All other pieces should not give a check to any king, so we find the colors of them.
4. There are 12 pawns and 6 queens, so 4 queens were created, all other pieces are original.
5. There are 2 white knights on the top, so the knight on g4 is black.

Then one needs to consider different possibilities of the pawns' placements, taking into account possible moves. It is hard for me to find a solid approach to it.

• Are there any more instructions? For example, should the kings not be in check?
– Simd
Commented Jun 6, 2014 at 10:28
• We need at least one colored chess piece to reduce it to one solution. Is the a reachable orientation within the game? Do we have 6 queens because 4 pawns are converted to queens? Commented Jun 6, 2014 at 12:51
• @kaine, no additional info. I believe this is enough. If you think otherwise - try to provide two different games (set of moves), which lead to this position. If you need a colour of any piece it is easy to find. Commented Jun 6, 2014 at 12:55
• @Lembik, no additional info. I don't understand your question about kings. Kings colours are easy to find. Commented Jun 6, 2014 at 12:55
• @klm123 So the answers to my questions are: a)you determine the difference between black and white because you assume the starting position closer to you is either black or white by some convention I am not familiar with and b) yes this is a position to be reached from the start of a regular game. Commented Jun 6, 2014 at 13:07

I've made some progress by looking at the number of captures (7) vs the number of pawns that have changed file. The extra f pawns can't have come from the left in only seven captures, so we should have four captures bringing them from the right. h->g x2 g->f x2 The extra d pawn must have come from the left, so we get at least one more capture. c->d And in order for the a and b pawns to no longer be there, a pawn must have moved from both (the other must have been promoted), although this doesn't tell us where the b pawn went to.

So that's all captures accounted for, and no pawn has left d, e or f. That means one white pawn must be below one black pawn in each file. And there is only one way to fill those six pawns in.

Since the extra f pawns came from the right, there can have been no promotions on the right side. So the f and g pawns all came from f, g and h. This means we need three white pawns and three black. We have two of each in f, so the g pawns must also be one of each.

Now suppose there were white pawns at e2 and g2. They must have been there the whole game, so the bishop that started at f1 could not have moved away, nor could it have been captured because no promotions happened on the right side. Since the bishop is no longer at f1, and we know the e2 pawn is white, the g2 pawn must be black. And hence the g3 pawn must be white.

We know that black made two captures on the right side to get its pawns across, and one further capture in order to have the second d pawn. Since the second black d pawn came from c, if the c pawn is also black, it must have come from b, which would mean a fourth capture for black. But black has only captured three pieces. So the c pawn must be white.

We've now located three white queens and six white pawns in total, so all the other queens must be black.

• a and b pawns could not be captured. We have 12 pawns + 4 extra queens. Commented Jun 6, 2014 at 15:05
• Oops, fixed. Thanks. Hopefully I haven't used mis-worded anything else - it was getting late. Commented Jun 7, 2014 at 3:16
• Seems to be correct... But I would add why f1 bishop had to be moved. Commented Jun 7, 2014 at 15:28
• Nicely done! If you want to see a diagram, check out my answer (not nearly as concise) to the same question at chess.SE! Commented Jun 8, 2014 at 4:21