Question

Problem 3 A magic square is a square array of natural numbers whose rows, columns, and diagonals all sum to the same number. For example, the following is a 3 by 3 magic square where the sums of the numbers in a row, a column, or a diagonal are all equal to 15. 4 9 2 3 5 7 8 1 6 Prove that it is impossible to construct a 3 by 3 magic square of the form a b c d 4 e f g h where every digit from 1 to 9 appears in this square one and only one time.

          Problem 3 A magic square is a square array of natural numbers whose rows, columns, and diagonals all sum to the same number. For example, the following is a 3 by 3 magic square where the sums of the numbers in a row, a column, or a diagonal are all equal to 15.
4 9 2
3 5 7
8 1 6
Prove that it is impossible to construct a 3 by 3 magic square of the form
a b c
d 4 e
f g h
where every digit from 1 to 9 appears in this square one and only one time.

Problem 3 A magic square is a square array of natural numbers whose rows, columns, and diagonals all sum to the same number. For example, the following is a 3 by 3 magic square where the sums of the numbers in a row, a column, or a diagonal are all equal to 15.
4 9 2
3 5 7
8 1 6
Prove that it is impossible to construct a 3 by 3 magic square of the form
a b c
d 4 e
f g h
where every digit from 1 to 9 appears in this square one and only one time.

Added by Stacey S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

11/26/2024

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Problem A magic square is a square array of natural numbers whose rows, columns, and diagonals all sum to the same number. For example, the following is a 3 by 3 magic square where the sums of the numbers in a row, a column, or a diagonal are all equal to 15. Prove that it is impossible to construct a 3 by 3 magic square of the form where every digit from 1 to 9 appears in this square one and only one time.