A magic square is an arrangement of n2 numbers into n rows and n columns using distinct numbers from 1 up to n2 such that the sum in any row, any column or any of the two diagonals is fixed. Consider the 4 by 4 magic square below:
a1 a5 2 13
a2 10 11 a7
a3 6 a4 12
4 15 a6 1
What is the value of a1 ?
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Answer:
A magic square is an arrangement of n^2 number into n rows and n columns using distinct numbers from 1 up to n^2 such that the sum in any row, any column or any of the two diagonals is fixed.
Step-by-step explanation:
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A magic square is an arrangement of n^2 number into n rows and n columns using distinct numbers from 1 up to n^2 such that the sum in any row, any column or any of the two diagonals is fixed. A magic square is an arrangement of n2 numbers into n rows and n columns using distinct numbers from 1 up to n2 such that the
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Transcribed image text: A magic square is an arrangement of n2 numbers into n rows and n columns using distinct numbers from 1 up to n2 such that the sum in any row, any column or any of the two diagonals is fixed. Consider the 4 by 4 magic square below: an a5 2 13 a2 10 11 az az 6 a4 12 4 15 a6 1 What is the value of a? O 16 O 5 09 07
Answer:
Step-by-step explanation:A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A magic square contains the integers from 1 to n2.
The constant sum in every row, column and diagonal are called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the following value:
M = n(n2+1)/2
For normal magic squares of order n = 3, 4, 5, ...,
the magic constants are: 15, 34, 65, 111, 175, 260, ...
Magic Square of size 3
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2 7 6
9 5 1
4 3 8
Sum in each row & each column = 3*(32+1)/2 = 15
Magic Square of size 5
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9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17
Sum in each row & each column = 5*(52+1)/2 = 65
Magic Square of size 7
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20 12 4 45 37 29 28
11 3 44 36 35 27 19
2 43 42 34 26 18 10
49 41 33 25 17 9 1
40 32 24 16 8 7 48
31 23 15 14 6 47 39
22 21 13 5 46 38 30
Sum in each row & each column = 7*(72+1)/2 = 175
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