justify that15 is the sum of eachrow of a 3X3 magic square using the number 0-9. Find the sume of all the numbers. What is the of eachrow in a 4X4 magic square that uses the numbers 1-16.
http://en.wikipedia.org/wiki/Magic_square
When you study the link given by bobpursely, make a note of
Albrecht Dürer's magic square, probably the most famous 4by4 magic square.
I especially like how, in the last row, he was able to insert the date of his "Melancolia" engraving as
1 15 14 4 to stand for 1514 AD
A being the first letter of the alphabet and D being the 4th letter, with 1514 the year
To justify that the sum of each row of a 3X3 magic square using the numbers 0-9 is 15, we can solve it step by step:
Step 1: Start by arranging the numbers 0-9 in a 3X3 grid, such as:
7 2 6
9 5 1
3 4 8
Step 2: Calculate the sum of each row:
Row 1: 7 + 2 + 6 = 15
Row 2: 9 + 5 + 1 = 15
Row 3: 3 + 4 + 8 = 15
As we can see, the sum of each row is indeed 15.
Now, let's move to a 4X4 magic square using the numbers 1-16:
Step 1: Arrange the numbers 1-16 in a 4X4 grid, such as:
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Step 2: Calculate the sum of each row:
Row 1: 16 + 3 + 2 + 13 = 34
Row 2: 5 + 10 + 11 + 8 = 34
Row 3: 9 + 6 + 7 + 12 = 34
Row 4: 4 + 15 + 14 + 1 = 34
As we can observe, the sum of each row is 34.
To find the sum of all the numbers in a 4X4 magic square, you can simply add up all the numbers in the square:
Sum = 16 + 3 + 2 + 13 + 5 + 10 + 11 + 8 + 9 + 6 + 7 + 12 + 4 + 15 + 14 + 1 = 136
Therefore, the sum of all the numbers in a 4X4 magic square is 136.