Pattern Programs and Series with Nested for Loops (ICSE Class 10 Java)

Understand Pattern Programs and Series with Nested for Loops

for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= 4; j++)
        System.out.print(i * j + " ");
    System.out.println();
}

Pattern Programs and Series with Nested for Loops: key facts

Row-and-column structure

• •Outer loop: rows
• •Inner loop: items of one row
• •println() after the inner loop

print() inside, println() outside the inner loop.

Total inner passes

Fixed inner count: outer passes multiplied by inner passes | Triangle of n rows: 1 + 2 + ... + n

For n = 4 the triangle needs 10 inner passes.

Jump statements in nested loops

break: leaves the innermost loop only | continue: skips the rest of the innermost pass

The outer loop continues normally.

Power series pattern

• •p = p times x
• •s = s + p
• •repeat n times

Start p = 1 and s = 0.

How to answer Pattern Programs and Series with Nested for Loops questions

1. 1List the values of the outer variable i.
2. 2For each i, work out the limits of the inner variable j (fixed, or depending on i).
3. 3Write the items printed by the inner loop on one line, using exactly the separators in print.
4. 4Look for println after the inner loop and break to the next line there.
5. 5Count total body passes by adding the inner counts of all rows.

Pattern Programs and Series with Nested for Loops in real life

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

Tricks to remember Pattern Programs and Series with Nested for Loops

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

• Clock hands

  The outer loop is the hour hand (slow), the inner loop the minute hand (fast): the minute hand does a full round for each hour step.

  Use it when: How nested loops run.

• print inside, println outside

  print() belongs inside the inner loop; println() goes after it.

  Use it when: Pattern layout.

• j <= i makes a triangle

  If the inner limit uses i, expect a triangle; if it is a constant, expect a rectangle.

  Use it when: Predicting a shape.

Pattern Programs and Series with Nested for Loops: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

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

for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= 4; j++)
        System.out.print(i * j + " ");
    System.out.println();
}

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

int c = 0;
for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= 3; j++) {
        if (j == 2)
            continue;
        if (i == 2)
            break;
        c++;
    }
}
System.out.println(c);

int x = 2, n = 4;
int s = 0, p = 1;
for (int i = 1; i <= n; i++) {
    p *= x;
    s += p;
}
System.out.println(s + " " + p);

Where students lose marks in Pattern Programs and Series with Nested for Loops

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

• ✗Mistake: Putting println() inside the inner loop

  Every item then goes on its own line.

  Wrong working

  for j ... { print(j); println(); }

  Right working

  for j ... print(j); println();

  ✓Do this: println after the inner loop.

  Usually costs: 1 mark

• ✗Mistake: Thinking break leaves both loops

  break leaves only the innermost loop.

  Wrong working

  After break at i = 2 the program stops.

  Right working

  After break at i = 2 the outer loop continues with i = 3.

  ✓Do this: Read break as "leave this loop only".

  Usually costs: 1 to 2 marks

• ✗Mistake: Skipping the separators in the output

  Spaces and the absence of spaces are part of the answer.

  Wrong working

  1234 for print(j + " ")

  Right working

  1 2 3 4

  ✓Do this: Copy the separator from the print statement.

  Usually costs: 1 mark

Practice questions on Pattern Programs and Series with 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

   How many times does the inner body run?
   for (int i = 1; i <= 3; i++)
   for (int j = 1; j <= 4; j++) { ... }
   (a) 7 (b) 12 (c) 4 (d) 3

   Hint

   Rows times columns.

   Answer

   (b) 12

2. Q2 · 1 mark · Very short answerBoard level

   In a nested for loop, which variable stays unchanged while the inner loop runs one full round?

   Hint

   Outer or inner?

   Answer

   The outer loop variable.

3. Q3 · 2 marks · Short answerHarder board level

   Write the output:

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

   Hint

   The inner loop starts from i.

   Answer

   123
   23
   3

4. Q4 · 3 marks · Short answerHarder board level

   Write nested loops that print the following pattern:
   4 3 2 1
   4 3 2
   4 3
   4

   Hint

   Every row starts at 4 and counts down; the stopping value rises with the row.

   Answer

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

5. Q5 · 1 mark · Assertion-reasonHOTS / competency

   Assertion (A): In a nested for loop, the inner loop completes all its passes for each pass of the outer loop.
   Reason (R): For a fixed inner count the total number of inner passes equals outer passes multiplied by inner passes.
   (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

   Hint

   Does R describe the total or explain the order?

   Answer

   (b) Both A and R are true but R is not the correct explanation of A. R gives the total count, while A describes the order of execution.

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.Which loop runs faster in a nested pair?Show answer

   The inner loop; it completes for every pass of the outer loop.

2. 2.What does println() after the inner loop do?Show answer

   Starts a new row.

3. 3.Which triangle is in the syllabus?Show answer

   The right-angled triangle.

4. 4.How many inner passes in a 4-row triangle 1,2,3,4?Show answer

   10

5. 5.What does break do in a nested loop?Show answer

   Leaves the innermost loop only.

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

   No, only nested for loops.

Pattern Programs and Series with Nested for Loops: frequently asked questions