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

Explanation : 

Chess Board Consecutive Squares Chosen

Given:
– Chess board has 2 diagonals with 8 squares each
– Need to select 6 consecutive squares
– These 6 squares must be consecutive along a diagonal

Step 1: Analyze one diagonal
– Diagonal has 8 squares
– Need to select 6 consecutive squares
– Think of 6 squares as one block
– This block can slide along diagonal

Step 2: Calculate possible positions on first diagonal
– 8 squares total, need 6 consecutive
– First position: squares 1-6
– Second position: squares 2-7
– Third position: squares 3-8
Total positions on first diagonal = 3

Step 3: Calculate possible positions on second diagonal
– Same calculation as first diagonal
– 3 possible positions
Total positions on second diagonal = 3

Step 4: Calculate total number of ways
– First diagonal: 3 ways
– Second diagonal: 3 ways
Total ways = 3 + 3 = 6