Nested for Loops ICSE Class 9: Patterns, Series, break and continue

What Nested for Loops is about

Weightage: CISCE publishes no chapter weightage and no question-paper layout for ICSE Class 9 Computer Applications. Class IX is examined by your school: one 100-mark theory paper of 2 hours, plus 100 marks of internal assessment (at least 15 programming assignments and a written project on ethical computing). This is topic 10 of the 2028 syllabus.Source: CISCE ICSE 2028 Computer Applications syllabus, Class IX

Key concepts

How a nested for loop executes

for (int i = 1; i <= rows; i++) // outer loop
{
for (int j = 1; j <= cols; j++) // inner loop
{
body;
}
}

Sequence: i = 1, then j runs 1 to cols completely; i = 2, then j starts again from 1 and runs completely; and so on. The inner loop is restarted from its initial value on every pass of the outer loop.

Counting iterations:

• Inner limit fixed: body runs rows × cols times (4 × 5 = 20).
• Inner loop depending on i, for example for (j = i; j <= 5; j++) inside for (i = 1; i <= 5; i++): passes are 5 + 4 + 3 + 2 + 1 = 15 (as run in this study guide: count = 15).

Real-life model: on a clock, the minute counter runs through all 60 minutes for every single step of the hour (outer loop: hours, inner loop: minutes); a teacher (outer) calls each row of the class, and in each row every student (inner) answers.

Worked example

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

Try it first, then show the solutionSolution

1. i = 1: j = 1..5 (5); i = 2: 4; i = 3: 3; i = 4: 2; i = 5: 1 - 1 mark.
2. Total = 5 + 4 + 3 + 2 + 1 = 15 - 1 mark.

Answer: 15 times

Square and rectangular patterns

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

Square of stars, 4 × 4 (as run in this study guide):
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= 4; j++)
System.out.print("* ");
System.out.println();
}
Output: four lines of * * * *

Rectangle printing the row number, 3 rows × 5 columns:
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 5; j++)
System.out.print(i);
System.out.println();
}
Output:
11111
22222
33333

Alternating 0 and 1 board, 3 × 4, using (i + j) % 2:
Output:
0101
1010
0101

What to print: print j for a column number, i for a row number, a fixed symbol, or a formula of i and j.

Worked example

(2 marks) Write nested loops to print 3 rows of 12345.

Try it first, then show the solutionSolution

1. Outer i = 1 to 3 (rows); inner j = 1 to 5 printing j - 1 mark.
2. println() after the inner loop - 1 mark.

Answer: for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 5; j++)
System.out.print(j);
System.out.println();
}

Right-angled triangle patterns with numbers

In a right-angled triangle the number of items changes from row to row, so the inner limit depends on the row number i.

Increasing triangle (as run in this study guide):
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= i; j++)
System.out.print(j);
System.out.println();
}
Output:
1
12
123
1234

Decreasing (inverted) triangle starting from 5:
for (int i = 1; i <= 4; i++)
{
for (int j = 5; j >= i + 1; j--)
System.out.print(j + " ");
System.out.println();
}
Output:
5 4 3 2
5 4 3
5 4
5

Numbers continuing across rows: keep a separate counter k that is never reset:
int k = 1;
for (int i = 1; i <= 4; i++)
{
for (int j = 1; j <= i; j++)
System.out.print(k++ + " ");
System.out.println();
}
Output:
1
2 3
4 5 6
7 8 9 10

Worked example

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

Try it first, then show the solutionSolution

1. Row i prints from i down to 1 - 1 mark.
2. Rows: 1 / 2 1 / 3 2 1 / 4 3 2 1 - 1 mark.

Answer: 1
2 1
3 2 1
4 3 2 1

Patterns with characters

Characters can be used as loop variables or produced from numbers with a cast.

Letters A, AB, ABC... (char as loop variable; as run in this study guide):
for (int i = 1; i <= 4; i++)
{
for (char c = 'A'; c < 'A' + i; c++)
System.out.print(c);
System.out.println();
}
Output:
A
AB
ABC
ABCD

Same letter repeated on each row:
for (int i = 1; i <= 4; i++)
{
char ch = (char) ('A' + i - 1);
for (int j = 1; j <= i; j++)
System.out.print(ch);
System.out.println();
}
Output:
A
BB
CCC
DDDD

Descending letters from E:
for (int i = 1; i <= 3; i++)
{
for (char c = 'E'; c > 'E' - i; c--)
System.out.print(c);
System.out.println();
}
Output:
E
ED
EDC

Remember: printing (char) ('A' + j) gives a letter; printing 'A' + j without a cast gives a number (65 + j).

Worked example

(2 marks) Write nested loops to print:
A
BB
CCC

Try it first, then show the solutionSolution

1. Outer i = 1 to 3; the letter for row i is (char) ('A' + i - 1) - 1 mark.
2. Inner loop prints it i times; println() after the inner loop - 1 mark.

Answer: for (int i = 1; i <= 3; i++)
{
char ch = (char) ('A' + i - 1);
for (int j = 1; j <= i; j++)
System.out.print(ch);
System.out.println();
}

break and continue inside nested loops

In nested loops, break and continue act only on the innermost loop that contains them; the outer loop carries on.

break in the inner loop (as run in this study guide):
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 4; j++)
{
if (j > i) break;
System.out.print(i * j + " ");
}
System.out.println();
}
Output:
1
2 4
3 6 9
The inner loop stops as soon as j exceeds i, which turns a rectangle loop into a triangle.

continue in the inner loop:
for (int i = 1; i <= 3; i++)
for (int j = 1; j <= 3; j++)
{
if (j == 2) continue;
System.out.print(i + "" + j + " ");
}
Output: 11 13 21 23 31 33
Only j = 2 is skipped in each row; the outer loop is unaffected.

Worked example

(2 marks) Does a break in the inner loop stop the outer loop? Explain with the output of the first program above.

Try it first, then show the solutionSolution

1. No; break exits only the inner loop - 1 mark.
2. The outer loop continues with the next i, giving rows 1 / 2 4 / 3 6 9 - 1 mark.

Answer: No. The break leaves only the inner loop; control returns to the outer loop, which goes on to the next row. So all three rows are printed: 1, then 2 4, then 3 6 9.

Series calculations and display

When each term of a series needs its own small calculation (a factorial, a sum), the outer loop goes through the terms and the inner loop calculates one term.

S = 1 + 1/2! + 1/3! + 1/4! + 1/5! (as run in this study guide):
double s = 0;
for (int i = 1; i <= 5; i++)
{
long f = 1; // reset for each term
for (int j = 1; j <= i; j++)
f = f * j;
s = s + 1.0 / f;
}
Result: s = 1.7166666666666668

Displaying a series 1, 3, 6, 10 (sums of 1..i):
for (int i = 1; i <= 4; i++)
{
int t = 0;
for (int j = 1; j <= i; j++)
t = t + j;
System.out.print(t + " ");
}
Output: 1 3 6 10

S = 1² + (1² + 2²) + (1² + 2² + 3²): adding j * j for j = 1..i for each i gives 1 + 5 + 14 = 20 (as run).

Key point: the variable for each term (f or t) must be reset inside the outer loop, before the inner loop starts.

Worked example

(2 marks) In the 1/n! series program, what goes wrong if long f = 1; is written before the outer loop instead of inside it?

Try it first, then show the solutionSolution

1. f is not reset, so each term multiplies onto the previous factorial - 1 mark.
2. Terms become 1, 1/2, 1/12, 1/288, ... instead of 1/1!, 1/2!, 1/3!, giving a wrong (smaller) sum - 1 mark.

Answer: Without resetting, f keeps growing: after term 2 it is 2, after term 3 it is 2 × 6 = 12, after term 4 it is 12 × 24 = 288, so the terms are 1, 1/2, 1/12, 1/288, ... and the sum is wrong. f must be set to 1 inside the outer loop for every term.

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

• Row and Column Patterns with Numbers, Characters and Spaces
• Series Programs and break and continue Inside Nested Loops

Nested for Loops: syntax and key facts

Pattern template

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

print inside, println after the inner loop.

Shape rule

Square/rectangle: limit fixed; right triangle: limit depends on i (j <= i, or j >= i)

Only right-angled triangles are in the syllabus.

Iterations

Fixed: rows × cols; triangle: 1 + 2 + … + n = n(n + 1)/2

n = 4 → 10; n = 7 → 28.

Letters

(char) ('A' + k) gives the (k + 1)th letter

Without the cast you get a number.

Jumps

break / continue affect only the innermost loop

Outer loop continues.

How the school exam 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.

• Rows outside, columns inside

  The outer loop says which line; the inner loop says what is on the line.

  Use it when: Every pattern.

• Triangle = j depends on i

  If each row has a different length, the inner limit uses i.

  Use it when: Right-angled triangles.

• Reset before the inner loop

  Anything calculated afresh for each row or term starts inside the outer loop.

  Use it when: Series and per-row sums.

Nested for Loops: exam-level solved questions

Ordered from exam 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 a school exam set on the board pattern this is a 8-mark question split into 2 + 3 + 3 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() inside the inner loop

  Not thinking about where a line ends.

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

  Usually costs: 2 to 3 marks in a program.

• ✗Mistake: Fixed inner limit for a triangle

  Square template copied.

  ✓Do this: Use i in the inner condition when rows have different lengths.

  Usually costs: 2 marks.

• ✗Mistake: Printing numbers instead of letters

  Missing cast.

  Wrong working

  System.out.print('A' + j); prints 65, 66, ...

  Right working

  System.out.print((char) ('A' + j));

  ✓Do this: Cast to char when doing arithmetic on letters.

  Usually costs: 1 to 2 marks.

• ✗Mistake: Not resetting a term variable

  Declared once before the outer loop.

  ✓Do this: Set f = 1 or t = 0 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 · MCQExam level

   How many times is the inner statement executed? for (int i = 1; i <= 3; i++) for (int j = 1; j <= 6; j++) x++;
   (a) 9
   (b) 18
   (c) 6
   (d) 3

   Hint

   3 × 6.

   Answer

   (b) 18

2. Q2 · 1 mark · MCQExam level

   Nested while and nested do-while loops in ICSE Class 9 are:
   (a) compulsory
   (b) exempted from the syllabus
   (c) only for patterns
   (d) only for series

   Hint

   Syllabus note.

   Answer

   (b) exempted from the syllabus

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

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

   Hint

   Even sum gives 0.

   Answer

   0101
   1010
   0101

4. Q4 · 2 marks · Very short answerHarder exam level

   Give the output: for (int i = 1; i <= 3; i++) { for (int j = 1; j <= 4; j++) { if (j > i) break; System.out.print(i * j + " "); } System.out.println(); }

   Hint

   break when j passes i.

   Answer

   1
   2 4
   3 6 9

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

   Write nested loops to print:
   5 4 3 2
   5 4 3
   5 4
   5

   Hint

   Inner from 5 down to i + 1.

   Answer

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

6. Q6 · 15 marks · Long answerHarder exam level

   Write a program using nested loops to find S = 1 + 1/2! + 1/3! + ... + 1/n!. What is S for n = 5?

   Hint

   Reset f for each term.

   Answer

   import java.util.*;
   class FactSeries
   {
   public static void main(String args[])
   {
   Scanner sc = new Scanner(System.in);
   System.out.print("n: ");
   int n = sc.nextInt();
   double s = 0;
   for (int i = 1; i <= n; i++)
   {
   long f = 1;
   for (int j = 1; j <= i; j++)
   f = f * j;
   s = s + 1.0 / f;
   }
   System.out.println("S = " + s);
   }
   }
   Sample run (as run, n = 5): S = 1.7166666666666668

7. Q7 · 2 marks · Very short answerExam level

   Write nested loops to display the series 1 3 6 10 15 (each term is the sum 1 + 2 + ... + i).

   Hint

   Reset t inside the outer loop.

   Answer

   for (int i = 1; i <= 5; i++)
   {
   int t = 0;
   for (int j = 1; j <= i; j++)
   t = t + j;
   System.out.print(t + " ");
   }

8. Q8 · 2 marks · Short answerHOTS / competency

   Find S = 1² + (1² + 2²) + (1² + 2² + 3²) using nested loops. Give the value.

   Hint

   Add j * j for j = 1..i.

   Answer

   int ss = 0; for (int i = 1; i <= 3; i++) for (int j = 1; j <= i; j++) ss = ss + j * j; Value: 1 + 5 + 14 = 20.

9. Q9 · 3 marks · Short answerHOTS / competency

   A student says, 'Any right-angled triangle pattern can be printed with a single loop if I use a long string.' Why does the syllabus still use nested loops, and what is the role of each loop?

   Hint

   General n.

   Answer

   A fixed string works only for one size; with nested loops the same code prints a pattern of any number of rows n entered by the user. The outer loop runs once per row, and the inner loop prints the items of that row, with a limit that depends on the row number.

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 a 4 × 5 nested loop?Show answer

   20

2. 2.Inner condition 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.Which triangles are in the syllabus?Show answer

   Right-angled triangles only.

5. 5.Expression giving the letter after 'A' by k places?Show answer

   (char) ('A' + k)

Quick revision checklist

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

• ☐Outer loop = rows; inner loop = items on a row.
• ☐Square/rectangle: inner limit fixed; right triangle: inner limit uses i.
• ☐print() inside, println() after the inner loop.
• ☐Letters: (char) ('A' + k).
• ☐break and continue act on the innermost loop only.
• ☐Series: reset term variables inside the outer loop; only nested for loops are in the syllabus.

Nested for Loops: frequently asked questions