Problem Statement: You need to find all possible solutions to place eight queens on a chess board - Condition is no two queens should be able to collide. Note: Queen can move diagonally or linearly to any length.

string answer = ""; int q1 = 0; int q2 = 0; int q3 = 0; int q4 = 0; int q5 = 0; int q6 = 0; int q7 = 0; int q8 = 0; int counter = 0; for ( q1 = 1; q1 < 9; q1++) { for ( q2 = 1; q2 < 9; q2++) { if ((q1 != q2)&& ( Math.Abs(q1 - q2) != 1 ) ) { for ( q3 = 1; q3 < 9; q3++) { if ((q1 != q3) && (q2 != q3) && (Math.Abs(q1 - q3) != 2) && (Math.Abs(q2 - q3) != 1)) { for ( q4 = 1; q4 < 9; q4++) { if ((q1 != q4) && (q2 != q4) && (q3 != q4) && (Math.Abs(q1 - q4) != 3) && (Math.Abs(q2 - q4) != 2) && (Math.Abs(q3 - q4) != 1)) { for ( q5 = 1; q5 < 9; q5++) { if ((q1 != q5) && (q2 != q5) && (q3 != q5) && (q4 != q5) && (Math.Abs(q1 - q5) != 4) && (Math.Abs(q2 - q5) != 3) && (Math.Abs(q3 - q5) != 2) && (Math.Abs(q4 - q5) != 1)) { for ( q6 = 1; q6 < 9; q6++) { if ((q1 != q6) && (q2 != q6) && (q3 != q6) && (q4 != q6) && (q5 != q6) && (Math.Abs(q1 - q6) != 5) && (Math.Abs(q2 - q6) != 4) && (Math.Abs(q3 - q6) != 3) && (Math.Abs(q4 - q6) != 2) && (Math.Abs(q5 - q6) != 1)) { for ( q7 = 1; q7 < 9; q7++) { if ((q1 != q7) && (q2 != q7) && (q3 != q7) && (q4 != q7) && (q5 != q7) && (q6 != q7) && (Math.Abs(q1 - q7) != 6) && (Math.Abs(q2 - q7) != 5) && (Math.Abs(q3 - q7) != 4) && (Math.Abs(q4 - q7) != 3) && (Math.Abs(q5 - q7) != 2) && (Math.Abs(q6 - q7) != 1)) { for ( q8 = 1; q8 < 9; q8++) { if ((q1 != q8) && (q2 != q8) && (q3 != q8) && (q4 != q8) && (q5 != q8) && (q6 != q8) && (q7 != q8) && (Math.Abs(q1 - q8) != 7) && (Math.Abs(q2 - q8) != 6) && (Math.Abs(q3 - q8) != 5) && (Math.Abs(q4 - q8) != 4) && (Math.Abs(q5 - q8) != 3) && (Math.Abs(q6 - q8) != 2) && (Math.Abs(q7 - q8) != 1)) { counter++; answer += counter.ToString() + ": " + "(1," + q1.ToString() + "),"+ "(2," + q2.ToString() + ")," + "(3," + q3.ToString() + ")," + "(4," + q4.ToString() + ")," + "(5," + q5.ToString() + ")," + "(6," + q6.ToString() + ")," + "(7," + q7.ToString() + ")," + "(8," + q8.ToString() + ")" + "\n\r"; } } } } } } } } } } } } } } } MessageBox.Show(answer ); label2.Text = answer;

Messagebox output: 1: (1,1),(2,5),(3,8),(4,6),(5,3),(6,7),(7,2),(8,4) 2: (1,1),(2,6),(3,8),(4,3),(5,7),(6,4),(7,2),(8,5) 3: (1,1),(2,7),(3,4),(4,6),(5,8),(6,2),(7,5),(8,3) 4: (1,1),(2,7),(3,5),(4,8),(5,2),(6,4),(7,6),(8,3) 5: (1,2),(2,4),(3,6),(4,8),(5,3),(6,1),(7,7),(8,5) 6: (1,2),(2,5),(3,7),(4,1),(5,3),(6,8),(7,6),(8,4) 7: (1,2),(2,5),(3,7),(4,4),(5,1),(6,8),(7,6),(8,3) 8: (1,2),(2,6),(3,1),(4,7),(5,4),(6,8),(7,3),(8,5) 9: (1,2),(2,6),(3,8),(4,3),(5,1),(6,4),(7,7),(8,5) 10: (1,2),(2,7),(3,3),(4,6),(5,8),(6,5),(7,1),(8,4) 11: (1,2),(2,7),(3,5),(4,8),(5,1),(6,4),(7,6),(8,3) 12: (1,2),(2,8),(3,6),(4,1),(5,3),(6,5),(7,7),(8,4) 13: (1,3),(2,1),(3,7),(4,5),(5,8),(6,2),(7,4),(8,6) 14: (1,3),(2,5),(3,2),(4,8),(5,1),(6,7),(7,4),(8,6) 15: (1,3),(2,5),(3,2),(4,8),(5,6),(6,4),(7,7),(8,1) 16: (1,3),(2,5),(3,7),(4,1),(5,4),(6,2),(7,8),(8,6) 17: (1,3),(2,5),(3,8),(4,4),(5,1),(6,7),(7,2),(8,6) 18: (1,3),(2,6),(3,2),(4,5),(5,8),(6,1),(7,7),(8,4) 19: (1,3),(2,6),(3,2),(4,7),(5,1),(6,4),(7,8),(8,5) 20: (1,3),(2,6),(3,2),(4,7),(5,5),(6,1),(7,8),(8,4) 21: (1,3),(2,6),(3,4),(4,1),(5,8),(6,5),(7,7),(8,2) 22: (1,3),(2,6),(3,4),(4,2),(5,8),(6,5),(7,7),(8,1) 23: (1,3),(2,6),(3,8),(4,1),(5,4),(6,7),(7,5),(8,2) 24: (1,3),(2,6),(3,8),(4,1),(5,5),(6,7),(7,2),(8,4) 25: (1,3),(2,6),(3,8),(4,2),(5,4),(6,1),(7,7),(8,5) 26: (1,3),(2,7),(3,2),(4,8),(5,5),(6,1),(7,4),(8,6) 27: (1,3),(2,7),(3,2),(4,8),(5,6),(6,4),(7,1),(8,5) 28: (1,3),(2,8),(3,4),(4,7),(5,1),(6,6),(7,2),(8,5) 29: (1,4),(2,1),(3,5),(4,8),(5,2),(6,7),(7,3),(8,6) 30: (1,4),(2,1),(3,5),(4,8),(5,6),(6,3),(7,7),(8,2) 31: (1,4),(2,2),(3,5),(4,8),(5,6),(6,1),(7,3),(8,7) 32: (1,4),(2,2),(3,7),(4,3),(5,6),(6,8),(7,1),(8,5) 33: (1,4),(2,2),(3,7),(4,3),(5,6),(6,8),(7,5),(8,1) 34: (1,4),(2,2),(3,7),(4,5),(5,1),(6,8),(7,6),(8,3) 35: (1,4),(2,2),(3,8),(4,5),(5,7),(6,1),(7,3),(8,6) 36: (1,4),(2,2),(3,8),(4,6),(5,1),(6,3),(7,5),(8,7) 37: (1,4),(2,6),(3,1),(4,5),(5,2),(6,8),(7,3),(8,7) 38: (1,4),(2,6),(3,8),(4,2),(5,7),(6,1),(7,3),(8,5) 39: (1,4),(2,6),(3,8),(4,3),(5,1),(6,7),(7,5),(8,2) 40: (1,4),(2,7),(3,1),(4,8),(5,5),(6,2),(7,6),(8,3) 41: (1,4),(2,7),(3,3),(4,8),(5,2),(6,5),(7,1),(8,6) 42: (1,4),(2,7),(3,5),(4,2),(5,6),(6,1),(7,3),(8,8) 43: (1,4),(2,7),(3,5),(4,3),(5,1),(6,6),(7,8),(8,2) 44: (1,4),(2,8),(3,1),(4,3),(5,6),(6,2),(7,7),(8,5) 45: (1,4),(2,8),(3,1),(4,5),(5,7),(6,2),(7,6),(8,3) 46: (1,4),(2,8),(3,5),(4,3),(5,1),(6,7),(7,2),(8,6) 47: (1,5),(2,1),(3,4),(4,6),(5,8),(6,2),(7,7),(8,3) 48: (1,5),(2,1),(3,8),(4,4),(5,2),(6,7),(7,3),(8,6) 49: (1,5),(2,1),(3,8),(4,6),(5,3),(6,7),(7,2),(8,4) 50: (1,5),(2,2),(3,4),(4,6),(5,8),(6,3),(7,1),(8,7) 51: (1,5),(2,2),(3,4),(4,7),(5,3),(6,8),(7,6),(8,1) 52: (1,5),(2,2),(3,6),(4,1),(5,7),(6,4),(7,8),(8,3) 53: (1,5),(2,2),(3,8),(4,1),(5,4),(6,7),(7,3),(8,6) 54: (1,5),(2,3),(3,1),(4,6),(5,8),(6,2),(7,4),(8,7) 55: (1,5),(2,3),(3,1),(4,7),(5,2),(6,8),(7,6),(8,4) 56: (1,5),(2,3),(3,8),(4,4),(5,7),(6,1),(7,6),(8,2) 57: (1,5),(2,7),(3,1),(4,3),(5,8),(6,6),(7,4),(8,2) 58: (1,5),(2,7),(3,1),(4,4),(5,2),(6,8),(7,6),(8,3) 59: (1,5),(2,7),(3,2),(4,4),(5,8),(6,1),(7,3),(8,6) 60: (1,5),(2,7),(3,2),(4,6),(5,3),(6,1),(7,4),(8,8) 61: (1,5),(2,7),(3,2),(4,6),(5,3),(6,1),(7,8),(8,4) 62: (1,5),(2,7),(3,4),(4,1),(5,3),(6,8),(7,6),(8,2) 63: (1,5),(2,8),(3,4),(4,1),(5,3),(6,6),(7,2),(8,7) 64: (1,5),(2,8),(3,4),(4,1),(5,7),(6,2),(7,6),(8,3) 65: (1,6),(2,1),(3,5),(4,2),(5,8),(6,3),(7,7),(8,4) 66: (1,6),(2,2),(3,7),(4,1),(5,3),(6,5),(7,8),(8,4) 67: (1,6),(2,2),(3,7),(4,1),(5,4),(6,8),(7,5),(8,3) 68: (1,6),(2,3),(3,1),(4,7),(5,5),(6,8),(7,2),(8,4) 69: (1,6),(2,3),(3,1),(4,8),(5,4),(6,2),(7,7),(8,5) 70: (1,6),(2,3),(3,1),(4,8),(5,5),(6,2),(7,4),(8,7) 71: (1,6),(2,3),(3,5),(4,7),(5,1),(6,4),(7,2),(8,8) 72: (1,6),(2,3),(3,5),(4,8),(5,1),(6,4),(7,2),(8,7) 73: (1,6),(2,3),(3,7),(4,2),(5,4),(6,8),(7,1),(8,5) 74: (1,6),(2,3),(3,7),(4,2),(5,8),(6,5),(7,1),(8,4) 75: (1,6),(2,3),(3,7),(4,4),(5,1),(6,8),(7,2),(8,5) 76: (1,6),(2,4),(3,1),(4,5),(5,8),(6,2),(7,7),(8,3) 77: (1,6),(2,4),(3,2),(4,8),(5,5),(6,7),(7,1),(8,3) 78: (1,6),(2,4),(3,7),(4,1),(5,3),(6,5),(7,2),(8,8) 79: (1,6),(2,4),(3,7),(4,1),(5,8),(6,2),(7,5),(8,3) 80: (1,6),(2,8),(3,2),(4,4),(5,1),(6,7),(7,5),(8,3) 81: (1,7),(2,1),(3,3),(4,8),(5,6),(6,4),(7,2),(8,5) 82: (1,7),(2,2),(3,4),(4,1),(5,8),(6,5),(7,3),(8,6) 83: (1,7),(2,2),(3,6),(4,3),(5,1),(6,4),(7,8),(8,5) 84: (1,7),(2,3),(3,1),(4,6),(5,8),(6,5),(7,2),(8,4) 85: (1,7),(2,3),(3,8),(4,2),(5,5),(6,1),(7,6),(8,4) 86: (1,7),(2,4),(3,2),(4,5),(5,8),(6,1),(7,3),(8,6) 87: (1,7),(2,4),(3,2),(4,8),(5,6),(6,1),(7,3),(8,5) 88: (1,7),(2,5),(3,3),(4,1),(5,6),(6,8),(7,2),(8,4) 89: (1,8),(2,2),(3,4),(4,1),(5,7),(6,5),(7,3),(8,6) 90: (1,8),(2,2),(3,5),(4,3),(5,1),(6,7),(7,4),(8,6) 91: (1,8),(2,3),(3,1),(4,6),(5,2),(6,5),(7,7),(8,4) 92: (1,8),(2,4),(3,1),(4,3),(5,6),(6,2),(7,7),(8,5)

Here are details of problem .

1) imagine rows 1,2,3,4,5,6,7,8

2) Now you want to place queens on 8 rows one in each row( one queeen per row :part of queens scope)

3) so each can be placed in any of 8 columns of each row.

4) when you place each one check it is not hitting any previously positioned queen.

5) Rest try to understand the code.

improve: Int can be replaced with tiny int. (one byte can represent 8 possibilities) This is a processor intesive and memory conservative algorithm. Bad: hardcoded 8 alla across. N queens on NXN square will be good problem to solve.