What is the sum of the 2 diagonals of a magic square with dimensions 7 × 7 ?
Note: Include the middle square twice.
Bonus : Construct your own 7 × 7 magic square.
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That seems like the smarter way to do it... I just found the mean of the set of numbers (1-49) and multiplied it by the amount of digits each row, column and diagonal should have, in this case a 7x7. Ends up working out to the same thing: The mean of odd numbered magic squares is also the median, in this case, 25. Multiply that by 7 (since this is a 7x7 square) to get 175; so every row/column/diagonal should add up to 175 each. The question asks for twice this, so 350 is the answer.
30 39 48 01 10 19 28
38 47 07 09 18 27 29
46 06 08 17 26 35 37
05 14 16 25 34 36 45
13 15 24 33 42 44 04
21 23 32 41 43 03 12
22 31 40 49 02 11 20
I did it by multiplying the magic constant by 2. Since it is a 7*7 magic square, magic constant will be (7x7x7+7)/2. Multiplying by 2, we get 175x2=350
sum of all numbers in this square: 1+2+...+(7 7)= 2 4 9 ∗ 5 0 \ sum of numbers in each diagonal: 2 4 9 ∗ 5 0 * 7 1 \ sum of numbers in two diagonals: 2 2 4 9 ∗ 5 0 * 7 1 =350
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If we add up all the numbers from 1 to 49 (Adding up all the square in our magic square) We will get 1225. As all the rows add up to the same number and all the rows cover all the squares, the sum of all the rows add to give 1225. Since there are 7 rows with equal values, each row adds to 1225/7 = 175. The diagonals have the same value as the rows so each diagonal adds to give 175 and since we have 2 diagonals of magic square, the sum of the diagonals is 2 x 175 = 350.