Albrecht Durer Inspired Magic Square
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A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n exactly once.
The normal magic square below is Albrecht Durer's famous magic square in which not only the rows, columns, and diagonals add up to s=34, but also the four corners and the inner opposite sides. Of particular note is that Mr. Durer created this magic square in 1514 and the middle of the bottom row also reads 1514.
So, in that spirit, I have decided to create a normal 5x5 magic square (s=65) with the number 2019 in the middle of the bottom row. Moreover, the inner cross squares (7, 2, 13, 24, 19) also add to 65. Here it is:
I have two questions:
(1) There are 275,305,224 valid normal 5x5 magic squares. How many of those contain (2019) in the middle of the bottom row?
(2) Note the inner 'x squares' (16, 22, 13, 15, 4) add up to 70. Can you give me an example of a normal 5x5 magic square where the 'x squares' also add up to s=65?
mathematics calculation-puzzle combinatorics grid-deduction magic-square
asked 6 mins ago
DiatcheDiatche
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A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n exactly once.
The normal magic square below is Albrecht Durer's famous magic square in which not only the rows, columns, and diagonals add up to s=34, but also the four corners and the inner opposite sides. Of particular note is that Mr. Durer created this magic square in 1514 and the middle of the bottom row also reads 1514.
So, in that spirit, I have decided to create a normal 5x5 magic square (s=65) with the number 2019 in the middle of the bottom row. Moreover, the inner cross squares (7, 2, 13, 24, 19) also add to 65. Here it is:
I have two questions:
(1) There are 275,305,224 valid normal 5x5 magic squares. How many of those contain (2019) in the middle of the bottom row?
(2) Note the inner 'x squares' (16, 22, 13, 15, 4) add up to 70. Can you give me an example of a normal 5x5 magic square where the 'x squares' also add up to s=65?
mathematics calculation-puzzle combinatorics grid-deduction magic-square
asked 6 mins ago
DiatcheDiatche
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n exactly once.
The normal magic square below is Albrecht Durer's famous magic square in which not only the rows, columns, and diagonals add up to s=34, but also the four corners and the inner opposite sides. Of particular note is that Mr. Durer created this magic square in 1514 and the middle of the bottom row also reads 1514.
So, in that spirit, I have decided to create a normal 5x5 magic square (s=65) with the number 2019 in the middle of the bottom row. Moreover, the inner cross squares (7, 2, 13, 24, 19) also add to 65. Here it is:
I have two questions:
(1) There are 275,305,224 valid normal 5x5 magic squares. How many of those contain (2019) in the middle of the bottom row?
(2) Note the inner 'x squares' (16, 22, 13, 15, 4) add up to 70. Can you give me an example of a normal 5x5 magic square where the 'x squares' also add up to s=65?
mathematics calculation-puzzle combinatorics grid-deduction magic-square
asked 6 mins ago
DiatcheDiatche
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n exactly once.
The normal magic square below is Albrecht Durer's famous magic square in which not only the rows, columns, and diagonals add up to s=34, but also the four corners and the inner opposite sides. Of particular note is that Mr. Durer created this magic square in 1514 and the middle of the bottom row also reads 1514.
So, in that spirit, I have decided to create a normal 5x5 magic square (s=65) with the number 2019 in the middle of the bottom row. Moreover, the inner cross squares (7, 2, 13, 24, 19) also add to 65. Here it is:
I have two questions:
(1) There are 275,305,224 valid normal 5x5 magic squares. How many of those contain (2019) in the middle of the bottom row?
(2) Note the inner 'x squares' (16, 22, 13, 15, 4) add up to 70. Can you give me an example of a normal 5x5 magic square where the 'x squares' also add up to s=65?
mathematics calculation-puzzle combinatorics grid-deduction magic-square
mathematics calculation-puzzle combinatorics grid-deduction magic-square
asked 6 mins ago
DiatcheDiatche
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
DiatcheDiatche
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
DiatcheDiatche
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 mins ago
DiatcheDiatche
12
asked 6 mins ago
DiatcheDiatche
12
12
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Diatche is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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