MAGIC SUM
Definition Of Magic Sum
Magic Sum is the sum that is obtained by adding the numbers in the horizontally-, vertically-, or diagonally-arranged blocks in a magic square.
More About Magic Sum
Magic sum is also called as magic constant.
Examples of Magic Sum
All the numbers that are horizontally, vertically, or diagonally arranged add up to 15. Therefore, the above square is a magic square and the sum 15 is called to be the magic sum.
Video Examples: Mathematics - Sum of 3 squares equals a 4th. Example uses fractions.
Solved Example on Magic Sum
Ques: Which of the following is called to be the magic sum of the figure shown?
Choices:
A. 34
B. 15
C. 30
D. 65
Correct Answer: A
Solution:
Step 1: Magic sum is the sum that is obtained by adding the numbers in the horizontally-, vertically-, or diagonally-arranged blocks in a magic square.
Step 2: Add up the numbers that are horizontally arranged.
1 + 15 + 14 + 4 = 34
12 + 6 + 7 + 9 = 34
8 + 10 + 11 + 5 = 34
13 + 3 + 2 + 16 = 34
Step 3: Add up the numbers that are vertically arranged.
1 + 12 + 8 + 13 = 34
15 + 6 + 10 + 3 = 34
14 + 7 + 11 + 2 = 34
4 + 9 + 5 + 16 = 34
Step 4: Add up the numbers that are diagonally arranged.
1 + 6 + 11 + 16 = 34
4 + 7 + 10 + 13 = 34
Step 5: So, the magic sum for the given figure is 34.
Quick Summary
- Magic sum is the constant sum obtained from rows, columns, and diagonals of a magic square.
- The magic sum depends on the size (order) of the magic square.
- It is also called the magic constant.
🍎 Teacher Insights
Use visual aids like colored blocks to represent numbers in the magic square and highlight the rows, columns, and diagonals being summed.🎓 Prerequisites
- Basic Addition
- Understanding of Square Grids
Check Your Knowledge
Q1: What is the magic sum of the following 3x3 magic square? [[8, 1, 6], [3, 5, 7], [4, 9, 2]]
Q2: A 4x4 magic square contains numbers 1 through 16. What is its magic sum?
Frequently Asked Questions
Q: How do you find the magic sum of a 3x3 magic square?
A: Calculate the sum of any row, column, or main diagonal. The result is the magic sum.
Q: Is there a formula for calculating the magic sum?
A: Yes, for a magic square of order n containing the numbers 1 to n^2, the magic sum is n(n^2 + 1)/2