Nested for Loops ICSE Class 10 Computer Applications

What Nested for Loops is about

Weightage: CISCE publishes no chapter weightage. Section A (40 marks) is compulsory: 1-mark MCQs and 2-mark short answers including output and error questions; in Section B you answer any four of six 15-mark programming questions written in Java.Source: CISCE ICSE Computer Applications (661) specimen paper structure for 2027

Key concepts

How nested loops run

In a nested loop, the inner loop is the body of the outer loop. For each value of the outer variable, the inner variable starts again and runs through all its values.

for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 2; j++)
System.out.print(i + "" + j + " ");
}
Output: 11 12 21 22 31 32

The body runs 3 × 2 = 6 times. Think of a clock: for each of the 12 hours (outer), the minute hand runs through all 60 minutes (inner).

For patterns: the outer loop controls rows (one pass per line) and the inner loop controls columns (what is printed on that line); println() after the inner loop moves to the next line.

Worked example

(2 marks) How many times is the statement inside executed? for (i = 1; i <= 4; i++) for (j = 1; j <= 5; j++) count++;

Try it first, then show the solutionSolution

1. Outer loop: 4 passes; inner: 5 passes each - 1 mark.
2. 4 × 5 = 20 - 1 mark.

Answer: 20 times

Rectangular patterns

In a rectangle every row has the same number of columns, so the inner loop's limit is fixed.

Rows of 1 2 3 4 5 (r = 4 rows, c = 5 columns):
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= 5; j++)
System.out.print(j + " ");
System.out.println();
}
Output:
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

Alternating symbols @#@#@ (4 rows): odd columns '@', even columns '#':
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= 5; j++)
{
if (j % 2 == 1) System.out.print("@");
else System.out.print("#");
}
System.out.println();
}
Output: @#@#@ on each of 4 lines.

Worked example

(2 marks) Give the output:
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 4; j++)
System.out.print(i);
System.out.println();
}

Try it first, then show the solutionSolution

1. Inner loop prints the row number i four times - 1 mark.
2. Three rows - 1 mark.

Answer: 1111
2222
3333

Right-angled triangle patterns

In a right-angled triangle the number of columns changes with the row, so the inner limit depends on i.

Increasing triangle (inner j <= i):
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= i; j++)
System.out.print(j + " ");
System.out.println();
}
Output:
1
1 2
1 2 3
1 2 3 4

Decreasing triangle (inner j <= 5 - i, or outer counting down):
for (int i = 4; i >= 1; i--)
{
for (int j = 1; j <= i; j++)
System.out.print("*");
System.out.println();
}
Output:
****
***
**
*

Floyd-style (numbers continue): use a separate counter k that is never reset:
int k = 1;
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= i; j++)
System.out.print(k++ + " ");
System.out.println();
}
Output:
1
2 3
4 5 6

Worked example

(2 marks) Write the loops to print:
5
5 4
5 4 3
5 4 3 2

Try it first, then show the solutionSolution

1. Outer i from 1 to 4 rows; each row starts at 5 - 1 mark.
2. Inner j from 5 down to 6 − i; print j; println after the inner loop - 1 mark.

Answer: for (int i = 1; i <= 4; i++)
{
for (int j = 5; j >= 6 - i; j--)
System.out.print(j + " ");
System.out.println();
}

break and continue in nested loops

break and continue act only on the innermost loop that contains them.

for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 3; j++)
{
if (j == 2) break;
System.out.print(i + "" + j + " ");
}
}
The break leaves only the inner loop each time; the outer loop continues. Output: 11 21 31

With continue instead of break, only j = 2 is skipped: 11 13 21 23 31 33

Worked example

(2 marks) Give the output:
for (int i = 1; i <= 2; i++)
{
for (int j = 1; j <= 3; j++)
{
if (i == j) continue;
System.out.print(i * j + " ");
}
}

Try it first, then show the solutionSolution

1. i = 1: j = 1 skipped; j = 2 → 2; j = 3 → 3 - 1 mark.
2. i = 2: j = 1 → 2; j = 2 skipped; j = 3 → 6 - 1 mark.

Answer: 2 3 2 6

Series with a single variable

Series programs add terms that depend on one variable (such as x or n).

Single loop: S = x + x²/2 + x³/3 + ... + xⁿ/n:
double s = 0;
for (int i = 1; i <= n; i++)
s = s + Math.pow(x, i) / i;

Nested loop (when each term needs its own inner calculation): S = 1! + 2! + 3! + ... + n!:
long s = 0;
for (int i = 1; i <= n; i++)
{
long f = 1;
for (int j = 1; j <= i; j++)
f = f * j;
s = s + f;
}
For n = 4: 1 + 2 + 6 + 24 = 33. The factorial f must be reset to 1 for each term (inside the outer loop).

Worked example

(2 marks) What is wrong if long f = 1; is placed before the outer loop in the factorial series program? What is printed for n = 3?

Try it first, then show the solutionSolution

1. f is never reset, so each term multiplies on top of the previous factorial - 1 mark.
2. Terms become 1, 1 × 1 × 2 = 2, 2 × 1 × 2 × 3 = 12; sum = 15 instead of 9 - 1 mark.

Answer: f must restart at 1 for each term. With f outside, the terms are 1, 2 and 12, so 15 is printed instead of the correct 1 + 2 + 6 = 9.

Nested for Loops in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Pattern Programs and Series with Nested for Loops

Nested for Loops: syntax and key facts

Iterations

Rectangle: rows × columns; triangle: 1 + 2 + … + n = n(n + 1)/2

Inner limit fixed → rectangle; depends on i → triangle.

Pattern template

for (i = 1; i <= rows; i++) { for (j = 1; j <= limit; j++) print(...); println(); }

print inside, println after the inner loop.

Jumps

break / continue affect only the innermost loop

How the board asks Nested for Loops

The question patterns to expect, and the method that works for each.

Tricks to remember Nested for Loops

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Outer rows, inner columns

  The outer loop is the number of lines; the inner loop is what goes on a line.

  Use it when: Every pattern.

• Triangle = j <= i

  If the row number decides how many items, the inner limit is i.

  Use it when: Right-angled triangles.

Nested for Loops: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In the board paper this is a 10-mark question split into 2 + 3 + 5 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Nested for Loops

The slips examiners see most often, and what to write instead.

• ✗Mistake: println() in both loops

  The 2025 examiners reported this in the @#@#@ pattern.

  ✓Do this: print() inside the inner loop; println() once after it.

  Usually costs: 2 to 3 marks of 15.

• ✗Mistake: Swapping outer and inner loops

  Also reported in 2025.

  ✓Do this: Outer = rows (lines), inner = columns (items per line).

  Usually costs: 2 to 3 marks.

• ✗Mistake: Forgetting println() after the inner loop

  The 2024 examiners noted this in the rows-of-numbers pattern.

  ✓Do this: Without it, all rows run together on one line.

  Usually costs: 1 to 2 marks.

• ✗Mistake: Not resetting inner accumulators

  Series terms that need an inner sum or factorial go wrong.

  ✓Do this: Initialise the term variable inside the outer loop.

  Usually costs: 2 to 4 marks.

Practice questions on Nested for Loops

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   In a pattern program, the outer loop usually controls the:
   (a) columns
   (b) rows
   (c) characters
   (d) spaces

   Hint

   Lines.

   Answer

   (b) rows

2. Q2 · 1 mark · MCQBoard level

   for (i = 1; i <= 5; i++) for (j = 1; j <= 3; j++) x++; If x starts at 0, its final value is:
   (a) 8
   (b) 15
   (c) 5
   (d) 3

   Hint

   5 × 3.

   Answer

   (b) 15

3. Q3 · 2 marks · Very short answerHarder board level

   Give the output:
   int k = 1;
   for (int i = 1; i <= 3; i++)
   {
   for (int j = 1; j <= i; j++)
   System.out.print(k++ + " ");
   System.out.println();
   }

   Hint

   k never resets.

   Answer

   1
   2 3
   4 5 6

4. Q4 · 2 marks · Short answerHOTS / competency

   Give the output:
   for (int i = 1; i <= 2; i++)
   {
   for (int j = 1; j <= 3; j++)
   {
   if (j == 2) continue;
   System.out.print(i + j + " ");
   }
   }

   Hint

   i + j is a number here.

   Answer

   2 4 3 5 (i = 1: j = 1 → 2, j = 3 → 4; i = 2: j = 1 → 3, j = 3 → 5)

5. Q5 · 2 marks · Very short answerHarder board level

   Write loops to print:
   A
   A B
   A B C
   A B C D

   Hint

   char arithmetic.

   Answer

   for (int i = 1; i <= 4; i++)
   {
   for (int j = 0; j < i; j++)
   System.out.print((char)('A' + j) + " ");
   System.out.println();
   }

6. Q6 · 15 marks · Long answerHarder board level

   Write a program to print the sum of the series S = 1 + (1 + 2) + (1 + 2 + 3) + ... up to n terms using nested loops.

   Hint

   Inner sum resets each term.

   Answer

   import java.util.Scanner;
   class TriSeries
   {
   public static void main(String args[])
   {
   Scanner sc = new Scanner(System.in);
   System.out.print("n: ");
   int n = sc.nextInt();
   int s = 0;
   for (int i = 1; i <= n; i++)
   {
   int t = 0;
   for (int j = 1; j <= i; j++)
   t = t + j;
   s = s + t;
   }
   System.out.println("Sum = " + s);
   }
   }
   Trace n = 4: terms 1, 3, 6, 10; Sum = 20.

7. Q7 · 15 marks · Long answerBoard level

   Write a program to accept n and print a right-angled triangle where row i contains the number i repeated i times (e.g. n = 3: 1 / 22 / 333).

   Hint

   Print i, not j.

   Answer

   import java.util.Scanner;
   class Repeat
   {
   public static void main(String args[])
   {
   Scanner sc = new Scanner(System.in);
   System.out.print("n: ");
   int n = sc.nextInt();
   for (int i = 1; i <= n; i++)
   {
   for (int j = 1; j <= i; j++)
   System.out.print(i);
   System.out.println();
   }
   }
   }
   Trace n = 3: 1 / 22 / 333.

8. Q8 · 2 marks · Short answerHOTS / competency

   Does break inside the inner loop stop the outer loop? Explain with an example.

   Hint

   Innermost only.

   Answer

   No. break exits only the loop that contains it. In for (i...) { for (j...) { if (j == 2) break; ... } } the inner loop stops at j = 2, but the outer loop carries on with the next i.

9. Q9 · 2 marks · Very short answerBoard level

   Why are nested while and nested do-while not examined?

   Hint

   Syllabus.

   Answer

   The 2027 syllabus limits nested loops to for loops; nested while and nested do-while are explicitly excluded.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Iterations of 4 × 5 nested loops?Show answer

   20

2. 2.Inner limit for a right-angled triangle?Show answer

   j <= i (depends on the row).

3. 3.Does continue in the inner loop skip the outer pass?Show answer

   No, only the current inner pass.

4. 4.Where does println() go in a pattern?Show answer

   After the inner loop, inside the outer loop.

5. 5.Are nested while loops in the syllabus?Show answer

   No.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Inner loop completes for every outer pass.
• ☐Rectangle: inner limit fixed; triangle: inner limit i.
• ☐print inside, println after inner.
• ☐break/continue affect the innermost loop only.
• ☐Reset term variables inside the outer loop for series.

Nested for Loops: frequently asked questions