Large magic square

Logic Level 3

What is the sum of the 2 diagonals of a magic square with dimensions $7 \times 7$ ?

Note: Include the middle square twice.

Bonus : Construct your own $7 \times 7$ magic square.

Details and Assumptions :

A magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number.

The answer is 350.

4 solutions

Josh Banister
Apr 9, 2015

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.

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.

Christopher Black - 6 years, 1 month ago

展豪張
Mar 14, 2016

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

Anoorag Nayak
Nov 23, 2015

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

Fateme Rahimi
Jan 13, 2019

sum of all numbers in this square: 1+2+...+(7 7)= $\frac{49*50}{2}$ \ sum of numbers in each diagonal: $\frac{49*50}{2}$ * $\frac{1}{7}$ \ sum of numbers in two diagonals: 2 $\frac{49*50}{2}$ * $\frac{1}{7}$ =350

Large magic square

The answer is 350.

4 solutions

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