On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path?

The question asks for the number of ways to choose 6 consecutive squares on the diagonals of a chessboard. An 8x8 chessboard has two main diagonals, each consisting of 8 squares. 1. **Identify the relevant diagonals:** The phrasing "the diagonals" in such problems often refers to the two main diagonals of the chessboard, especially when other interpretations lead to answers not among the options. Each main diagonal on an 8x8 chessboard has a length of 8 squares. 2. **Calculate ways for each main diagonal:** * For the first main diagonal (e.g., A1-H8), which has 8 squares: To choose 6 consecutive squares, we can start at the 1st, 2nd, or 3rd square. The possible starting squares are: 1. A1 (sequence: A1-B2-C3-D4-E5-F6) 2. B2 (sequence: B2-C3-D4-E5-F6-G7) 3. C3 (sequence: C3-D4-E5-F6-G7-H8) This gives 3 different ways. (Alternatively, Length - SegmentLength + 1 = 8 - 6 + 1 = 3 ways). * For the second main diagonal (e.g., A8-H1), which also has 8 squares: Similarly, there are 3 different ways to choose 6 consecutive squares: 1. A8 (sequence: A8-B7-C6-D5-E4-F3) 2. B7 (sequence: B7-C6-D5-E4-F3-G2) 3. C6 (sequence: C6-D5-E4-F3-G2-H1) 3. **Total ways:** Summing the ways from both main diagonals: 3 + 3 = 6 ways. Therefore, there are 6 different ways to choose 6 consecutive squares on the two main diagonals of a chessboard. The final answer is B) 6