# **Magic Square for Class 5 Maths**

The magic square represents a square that contains distinct integers. Here students will learn about Ramanujan magic square and magic square examples such as magic square 4 × 4, magic square 3 × 3, and magic square question. Also, about the Ramanujan magic square. That also connects students with the mathematical concept of addition and subtraction of numbers, calendars, etc.

## What Is Magic Square?

A square is said to be a magic square if the

The sum of the numbers along the columns,

rows and the diagonals of the

square is the same.

## Ramanujan Magic Square:

Ramanujan was a great

mathematician. He made a magic

square with four rows and four

columns.

His birthday was on 22nd December 1887 (22/12/18 87). He made a magic square so that the numbers in the first row represent his birthday.

**Characteristics of Ramanujan Magic Square:**

1. Sum of the numbers in any of the

four rows are equal to 139.

2. Sum of the numbers in any of the

four columns are equal to 139.

3. Sum of the numbers in any of the

two diagonal is equal to 139.

4. Sum of the numbers that are in

the corners is 139.

5. Sum of the numbers that are

in the boxes of the same colour is

139.

6. Sum of the numbers in the

The central square is equal to 139.

7. Sum of the numbers in the

in the squares of the same

colours are equal to 139.

8. Sum of the numbers in the

in the squares of the same

colours are equal to 139.

General Form:

## How to Make a Magic Square:

- The numbers in the first row should be as follows:
- The number in the second row should be as follows:
- The number in the second row should be as follows:
- The number in the second row should be as follows:

Hence, Ramanujan’s Magic square is of the form:

Here, DD = Date of birth.

MM= Month of birth.

CC= Century of birth.

YY= Year of birth.

**Calendar Math’s Tricks:**

## Question 1:

Saiqua’s Birthday Is on 02 April 1995. Draw a Saiqua’s Magic Square.

### Answer 1:

Since Saiqua’s birthday is on 02 April 1995.

We have DD = 02

MM = 04

CC = 19

YY = 95

Using the concept of Ramanujan’s Magic square, we have,

The numbers in the first row should be:

02, 04, 19, 95

The numbers in the second row should be:

95 + 1 = 96, 19 – 1 = 18, 04 – 3 = 01, 02 + 3 = 05

The numbers in the third row should be:

04 – 2 = 02, 02 + 2 = 4, 95 + 2 = 97, 19 – 2 = 17

The numbers in the fourth row should be:

19 + 1 = 20, 95 – 1 = 94, 02 + 1 = 03, 04 – 1 = 03

Therefore, the magic square is:

## Question 2:

Rina Created a Magic Square Based on Her Birthday, Which Is On 12-12-2010 As Given Below.

Seema Said That It Was Incorrect As the Sum of the Numbers in Each Column Was Not Equal.

Find Out the Mistakes and Also Draw the Correct Magic Square.

### Answer 2:

Magic Square, created by Rina, was:

It is observed from the numbers in the first row are as follows:

DD, MM, CC, YY.

The numbers in the second row are as follows:

CC – 1, YY + 1, MM – 3, DD + 3, whereas the correct order is

YY + 1. CC – 1, MM – 3, DD + 3.

The numbers in the third row are as follows:

MM – 2, DD + 2, CC – 2, YY + 2, whereas the correct order is

MM – 2, DD + 2, YY + 2, CC – 2.

The numbers in the fourth row are as follows:

YY – 1, CC + 1, DD + 1, MM – 1, whereas the correct order is

CC + 1, YY – 1, DD + 1, MM – 1

Therefore, it is observed that Rina has interchanged the position of CC and YY from the second row to the fourth row.

The correct magic square is shown below:

## Question 3:

Help Sharukh to complete the Magic Square for His Pet Dog Tommy’s Birthday.

### Answer 3:

From the first row, it is observed that:

DD = 08

MM = 10

CC = 19

YY = 90

The numbers in the second row should be as follows:

YY + 1. CC – 1, MM – 3, DD + 3, that is,

91, 18, 07, 11. Therefore, the missing numbers in the second row are 91 and 11.

The numbers in the third row should be as follows:

MM – 2, DD + 2, YY + 2, CC – 2, that is,

08, 10, 92, 17. Therefore, the missing numbers in the third row are 08 and 92.

The numbers in the fourth row should be as follows:

CC + 1, YY – 1, DD + 1, MM – 1, that is

20, 89, 09, 09. Therefore, the missing numbers in the third row are 89 and 09.

The complete magic box is shown below.

**Addition and Subtraction Sums**

## Question 4:

Use the Digits 5, 12, 15, and 16 to Complete the Square, Such That the Sum in Each Row and Each Column Is Equal to 34.

### Answer 4:

Step 1: The sum of the given numbers in the first row is:

2 + 13 + 3 = 18

The total sum of the numbers in the first row = 34.

The sum of the given numbers = 18

Missing numbers = 34 – 18

= 16

Therefore, the missing number in the first row is 16.

Step 2: The sum of the given numbers in the second row is:

11 + 8 + 10 = 29

The total sum of the numbers in the second row = 34.

The sum of the given numbers = 29

Missing numbers = 34 – 29

= 5

Therefore, the missing number in the second row is 5.

Step 3: The sum of the given numbers in the third row is:

7 + 9 + 6 = 22

The total sum of the numbers in the third row = 34.

The sum of the given numbers = 22

Missing numbers = 34 – 22

= 12

Therefore, the missing number in the third row is 12.

Step 4: The sum of the given numbers in the fourth row is:

14 + 4 + 1 = 19

The total sum of the numbers in the fourth row = 34.

The sum of the given numbers = 19

Missing numbers = 34 – 19

= 15

Therefore, the missing number in the fourth row is 15.

Step 5: The complete square is:

## Question 5:

Suresh Was Born in 1890 in the Fifth Month of the Year. The Birth Date of Suresh Is 10 Days More Than the 12th of May. Calculate the Birthday of Suresh and Draw a Magic Square Using Suresh’s Birthday.

### Answer 5:

Birthday year = 1890

CC = 18

YY = 90

Birthday month = 5th month = May

MM = 05

Birthday date = 10 + 12 = 22.

DD = 22

The numbers in the first row are as follows:

22, 05, 18, 90

The number in the second row are as follows:

90 + 1 = 91, 18 – 1 = 17, 05 – 03 = 02, 22 + 3 = 25

The numbers in the third row are as follows:

05 – 02 = 03, 22 + 2 = 24, 90 + 2 = 92, 18 – 2 = 16

The numbers in the fourth row are as follows:

18 + 1 = 19, 90 – 1 = 89, 22 + 1 = 23, 05 – 1 = 04

The complete square is