MAGIC SQUARE
The real magic isn't the square...it's how we change minds about math!
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The magic square shown contains each of the positive integers 1-25. The sum of the numbers in each row, each column and both diagonals is the same. What is the value of n?
Let’s start by finding the sum of the positive integers 1, 2, 3, …, 25. Notice we can pair up the integers into sums of 26: 1 and 25, 2 and 24, 3 and 23, and so on. There are 12 of these pairs, with the integer 13 left in the middle with no partner. The sum of the 25 integers, then, is 26 × 12 + 13 = 312 + 13 = 325. Because each of the five rows must have the same sum, we can determine that sum to be 325 ÷ 5 = 65. Adding the known values in the 4th row, we get 10 + 12 + 21 + 3 = 46. Therefore, the value of n is 65 − 46 = 19.
