Row and Column Patterns with Numbers, Characters and Spaces Using Nested for Loops (ICSE Class 9)

Understand Row and Column Patterns with Numbers, Characters and Spaces

Row and Column Patterns with Numbers, Characters and Spaces: key facts

Iterations

rows times columns for a rectangle | 1 + 2 + ... + n for a triangle

Inner body count.

Row end

println() goes after the inner loop | not inside it

Otherwise every symbol is on its own line.

Right-aligned triangle

• •spaces: n - i
• •symbols: i
• •on row i

Two inner loops.

Letter of the row

(char) (65 + i) gives A, B, C for i = 0, 1, 2 | cast back from int

A is 65.

How to answer Row and Column Patterns with Numbers, Characters and Spaces questions

1. 1Decide the number of rows and write what each row looks like.
2. 2Choose the outer loop for the rows.
3. 3Decide how many items each row has in terms of the row variable and write the inner loop.
4. 4Decide what to print (a symbol, i, j or a character).
5. 5Put println() after the inner loop and trace the first two rows to check.

Row and Column Patterns with Numbers, Characters and Spaces 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 Row and Column Patterns with Numbers, Characters and Spaces

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

• Rows outside, columns inside

  The outer loop is the row; the inner loop is the column.

  Use it when: Structure.

• Println ends the row

  Put println() after the inner loop.

  Use it when: Layout.

• Limit of the inner loop is the shape

  Fixed gives a rectangle; row variable gives a triangle.

  Use it when: Shapes.

Row and Column Patterns with Numbers, Characters and Spaces: solved examples

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

for (int i = 1; i <= 5; i++)
for (int j = 1; j <= 3; j++)
System.out.print("*");

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

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

for (int r = 1; r <= 3; r++)
{
for (int c = 1; c <= 4; c++)
System.out.print("R" + r + "C" + c + " ");
System.out.println();
}

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

Where students lose marks in Row and Column Patterns with Numbers, Characters and Spaces

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

• ✗Mistake: println inside the inner loop

  Every symbol is on a new line.

  Wrong working

  Each star on its own line

  Right working

  println() after the inner loop

  ✓Do this: Rows end after the inner loop.

  Usually costs: 2 marks

• ✗Mistake: Resetting the wrong variable

  The inner variable is declared outside.

  Wrong working

  j declared before the outer loop and not reset

  Right working

  Initialise j in the inner for header

  ✓Do this: The inner loop must restart for every row.

  Usually costs: 2 marks

• ✗Mistake: Forgetting to cast a char

  A char plus an int is an int.

  Wrong working

  print('A' + i) prints a number

  Right working

  print((char) ('A' + i))

  ✓Do this: Cast back to char.

  Usually costs: 1 mark

Practice questions on Row and Column Patterns with Numbers, Characters and Spaces

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

   Where should System.out.println() be placed to end each row in a nested loop pattern?
   (a) inside the inner loop (b) after the inner loop, inside the outer loop (c) before the outer loop (d) after the outer loop

   Hint

   One new line per row.

   Answer

   (b) after the inner loop, inside the outer loop

2. Q2 · 1 mark · Very short answerBoard level

   How many times does the body run in for (i = 1; i <= 4; i++) for (j = 1; j <= 4; j++)?

   Hint

   Rows times columns.

   Answer

   16

3. Q3 · 3 marks · Short answerHarder board level

   Show 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

   1 2 3
   2 3
   3

4. Q4 · 3 marks · Short answerHarder board level

   Write nested loops that print
   1 2 3 4
   1 2 3
   1 2
   1

   Hint

   The inner limit decreases.

   Answer

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

5. Q5 · 4 marks · Short answerHOTS / competency

   For (i) for (i = 1; i <= 4; i++) for (j = i; j <= 4; j++) and (ii) the multiplication pattern for i = 1 to 3 and j = 1 to 3 printing i * j and a space, find the number of inner executions in (i) and show the output of (ii).

   Hint

   Count 4 + 3 + 2 + 1.

   Answer

   (i) i = 1 gives 4 passes, i = 2 gives 3, i = 3 gives 2, i = 4 gives 1: 10 executions. (ii) 1 2 3 on the first line, 2 4 6 on the second, 3 6 9 on the third.

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 gives the rows?Show answer

   The outer loop.

2. 2.How often does the inner loop restart?Show answer

   Once for every pass of the outer loop.

3. 3.Inner body executions for 3 rows and 4 columns?Show answer

   12

4. 4.Which statement ends a row?Show answer

   System.out.println();

5. 5.Limit of the inner loop for an increasing triangle?Show answer

   j <= i

6. 6.How to print the letter C from i = 2?Show answer

   (char) ('A' + i)

Row and Column Patterns with Numbers, Characters and Spaces: frequently asked questions