8, for one possible solution, place the queens on the squares; f1,c2,e3,g4,a1,d4,b2,h8. As Cambsman has pointed out this solution is not correct. It should read f1,c2,e3,g4,a5,d6,b7,h8.

What is throwing me on the question is the line ... "on the next move" - so i will answer the how I think you meant. On a 8x8 chess board there are 92 ways to place 8 queen as to where none can capture any other. 1 - 1 5 8 6 3 7 2 4 2 - 1 6 8 3 7 4 2 5 3 - 1 7 4 6 8 2 5 3 4 - 1 7 5 8 2 4 6 3 5 - 2 4 6 8 3 1 7 5 6 - 2 5 7 1 3 8 6 4 7 - 2 5 7 4 1 8 6 3 8 - 2 6 1 7 4 8 3 5 9 - 2 6 8 3 1 4 7 5 10 - 2 7 3 6 8 5 1 4 11 - 2 7 5 8 1 4 6 3 12 - 2 8 6 1 3 5 7 4 13 - 3 1 7 5 8 2 4 6 14 - 3 5 2 8 1 7 4 6 15 - 3 5 2 8 6 4 7 1 16 - 3 5 7 1 4 2 8 6 17 - 3 5 8 4 1 7 2 6 18 - 3 6 2 5 8 1 7 4 19 - 3 6 2 7 1 4 8 5 20 - 3 6 2 7 5 1 8 4 21 - 3 6 4 1 8 5 7 2 22 - 3 6 4 2 8 5 7 1 23 - 3 6 8 1 4 7 5 2 24 - 3 6 8 1 5 7 2 4 25 - 3 6 8 2 4 1 7 5 26 - 3 7 2 8 5 1 4 6 27 - 3 7 2 8 6 4 1 5 28 - 3 8 4 7 1 6 2 5 29 - 4 1 5 8 2 7 3 6 30 - 4 1 5 8 6 3 7 2 31 - 4 2 5 8 6 1 3 7 32 - 4 2 7 3 6 8 1 5 33 - 4 2 7 3 6 8 5 1 34 - 4 2 7 5 1 8 6 3 35 - 4 2 8 5 7 1 3 6 36 - 4 2 8 6 1 3 5 7 37 - 4 6 1 5 2 8 3 7 38 - 4 6 8 2 7 1 3 5 39 - 4 6 8 3 1 7 5 2 40 - 4 7 1 8 5 2 6 3 41 - 4 7 3 8 2 5 1 6 42 - 4 7 5 2 6 1 3 8 43 - 4 7 5 3 1 6 8 2 44 - 4 8 1 3 6 2 7 5 45 - 4 8 1 5 7 2 6 3 46 - 4 8 5 3 1 7 2 6 47 - 5 1 4 6 8 2 7 3 48 - 5 1 8 4 2 7 3 6 49 - 5 1 8 6 3 7 2 4 50 - 5 2 4 6 8 3 1 7 51 - 5 2 4 7 3 8 6 1 52 - 5 2 6 1 7 4 8 3 53 - 5 2 8 1 4 7 3 6 54 - 5 3 1 6 8 2 4 7 55 - 5 3 1 7 2 8 6 4 56 - 5 3 8 4 7 1 6 2 57 - 5 7 1 3 8 6 4 2 58 - 5 7 1 4 2 8 6 3 59 - 5 7 2 4 8 1 3 6 60 - 5 7 2 6 3 1 4 8 61 - 5 7 2 6 3 1 8 4 62 - 5 7 4 1 3 8 6 2 63 - 5 8 4 1 3 6 2 7 64 - 5 8 4 1 7 2 6 3 65 - 6 1 5 2 8 3 7 4 66 - 6 2 7 1 3 5 8 4 67 - 6 2 7 1 4 8 5 3 68 - 6 3 1 7 5 8 2 4 69 - 6 3 1 8 4 2 7 5 70 - 6 3 1 8 5 2 4 7 71 - 6 3 5 7 1 4 2 8 72 - 6 3 5 8 1 4 2 7 73 - 6 3 7 2 4 8 1 5 74 - 6 3 7 2 8 5 1 4 75 - 6 3 7 4 1 8 2 5 76 - 6 4 1 5 8 2 7 3 77 - 6 4 2 8 5 7 1 3 78 - 6 4 7 1 3 5 2 8 79 - 6 4 7 1 8 2 5 3 80 - 6 8 2 4 1 7 5 3 81 - 7 1 3 8 6 4 2 5 82 - 7 2 4 1 8 5 3 6 83 - 7 2 6 3 1 4 8 5 84 - 7 3 1 6 8 5 2 4 85 - 7 3 8 2 5 1 6 4 86 - 7 4 2 5 8 1 3 6 87 - 7 4 2 8 6 1 3 5 88 - 7 5 3 1 6 8 2 4 89 - 8 2 4 1 7 5 3 6 90 - 8 2 5 3 1 7 4 6 91 - 8 3 1 6 2 5 7 4 92 - 8 4 1 3 6 2 7 5

It seems to me that this question could be approached differently. Assuming that queens of the same color wouldn't take each other, one could place many more queens on the board. 64 of either color. Also...

I get 8, IN POSITION, but on the NEXT move it could only be 7

dam it, I have found ppl smarter than I, life is good.

64 black ones, or 64 white ones haha.

18 (God I need to get a life) There have been some good answers - but I thought I would try and anwer this as if it was a game of chess rather than a board where we can just drop queens on to it. So how many queens could we manouever in a game of chess to get maximum number on board so that they dont take each other. 0000kqqq 00000qqq 00000qqq 0000nnrr RRNN0000 QQQ00000 QQQ00000 QQQK0000 Working out:- OK taking into account that the maximum number of queens white can have is 9 and that black can have is 9. So that would imply a maximum of 18 queens possible. It took me a while but it is possible for all 16 pawns to get promoted (imagine white taking to the right and black taking to his right on every other row - 4 pieces from each side other than a pawn or a queen being sacrificed. there will then be 2 pawns of the same colour on each column (alternate colours). So we could have 18 queens left on the board and two kings and each side having 4 other peices left - lets make them nights and rooks. So lets put whites queens in a 3x3 grid in the corner :- a1 a2 a3 b1 b2 b3 c1 c2 c3 We can place blacks queens in the opposite corner f6 f7 f8 g6 g7 g8 h6 h7 h8 Some of the queens are attacking ewach other - so we can easily stop that by using the rooks and nights. Place whites rooks on a4 and b4 and the nights on c4 and d4 Similar for black rooks on h5 and g5 with the nights on f5 and e5 Now we need to palce the kins where thay cant be taken:- White king on d1 and black king on e8. So maximum possible in a match would be 18.

8 on a 8x8 chess grid....