Q.Program 6-8: Program to print even numbers in a given sequence using for loop.

Nested For Loops: Loops Inside Loops

Imagine you're a teacher taking attendance in a school with 3 classrooms, each having 5 students. You go to Room 1, call out all 5 names, then move to Room 2, call out all 5 names, then Room 3, call out all 5 names. That's a loop inside a loop — for each classroom, you run through all students.

That's the entire intuition. A nested for loop is simply a for loop placed inside the body of another for loop. The outer loop runs once, and for that single iteration, the inner loop runs completely from start to finish. Then the outer loop moves to its next iteration, and the inner loop runs completely again.

The Precise Statement

for i in range(3):          # outer loop
    for j in range(5):      # inner loop
        print(i, j)

Here's exactly what happens, step by step:

1. i becomes 0. Enter the inner loop.
2. j runs through 0, 1, 2, 3, 4 — printing each pair (0,0), (0,1), ..., (0,4).
3. Inner loop finishes. i becomes 1. Enter the inner loop again.
4. j runs through 0, 1, 2, 3, 4 again — printing (1,0), (1,1), ..., (1,4).
5. Inner loop finishes. i becomes 2. Inner loop runs a third time.
6. j runs through 0, 1, 2, 3, 4 — printing (2,0), ..., (2,4).

Total printed lines: $3 \times 5 = 15$.

Why This Matters

Nested loops are how you work with tables, grids, matrices, and any data that has rows and columns. A 2D list (like a spreadsheet) is naturally processed with one loop for rows and another for columns.

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
for row in matrix:          # outer: pick a row
    for element in row:     # inner: pick each element in that row
        print(element, end=' ')
    print()                 # new line after each row

Output:

1 2 3 
4 5 6 
7 8 9 

The outer loop selects a row; the inner loop walks across that row's elements. When the inner loop finishes, the outer loop moves to the next row.

Common Mistake …