Question

A normal magic square of order n is a square array having n horizontal rows and n vertical rows, in which the n2 entries are precisely the positive integers 1 through n2, such that the sum of the entries along any row, column, or diagonal is equal to the same value, kn. (a) Show that, in a normal magic square of order 3, the entry in row 2 and column 2 must be 5. (b) Show that, in a normal magic square of order 3, the entry in any of the four corner positions cannot be 1.

Name: a normal magic square of order n is a square array having n horizontal rows and n vertical rows in which the n2 entries are precisely the positive integers 1 through n2 such that the sum of 66597
Uploaded: 2023-03-09T09:37:57-08:00
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Description: a normal magic square of order n is a square array having n horizontal rows and n vertical rows in which the n2 entries are precisely the positive integers 1 through n2 such that the sum of 66597

          A normal magic square of order n is a square array having n horizontal rows and n vertical rows, in which the n2 entries are precisely the positive integers 1 through n2, such that the sum of the entries along any row, column, or diagonal is equal to the same value, kn. 
(a) Show that, in a normal magic square of order 3, the entry in row 2 and column 2 must be 5.
(b) Show that, in a normal magic square of order 3, the entry in any of the four corner positions cannot be 1.

Added by Daniel C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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A normal magic square of order n is a square array having n horizontal rows and n vertical rows, in which the n2 entries are precisely the positive integers 1 through n2, such that the sum of the entries along any row, column, or diagonal is equal to the same value, kn. (a) Show that, in a normal magic square of order 3, the entry in row 2 and column 2 must be 5. (b) Show that, in a normal magic square of order 3, the entry in any of the four corner positions cannot be 1.